Advanced Structural Inorganic Chemistry (International Union of Crystallography Texts on Crystallography)

I N T E R N AT I O N A L U N I O N O F C R Y S TA L L O G R A P H Y T E X T S O N C R Y S TA L L O G R A P H Y

IUCr BOOK SERIES COMMITTEE E. N. Baker, New Zealand J. Bernstein, Israel G. R. Desiraju, India A. M. Glazer, UK J. R. Helliwell, UK P. Paufler, Germany H. Schenk (Chairman), The Netherlands

IUCr Monographs on Crystallography 1 Accurate molecular structures A. Domenicano and I. Hargittai, editors 2 P. P. Ewald and his dynamical theory of X-ray diffraction D. W. J. Cruickshank, H. J. Juretschke, and J. Kato, editors 3 Electron diffraction techniques, Volume 1 J. M. Cowley, editor 4 Electron diffraction techniques Volume 2 J. M. Cowley, editor 5 The Rietveld method R. A. Young, editor 6 Introduction to crystallographic statistics U. Shmueli and G. H. Weiss 7 Crystallographic instrumentation L. A. Aslanov, G. V. Fetisov, and G. A. K. Howard 8 Direct phasing in crystallography C. Giacovazzo 9 The weak hydrogen bond G. R. Desiraju and T. Steiner 10 Defect and microstructure analysis by diffraction R. L. Snyder, J. Fiala, and H. J. Bunge 11 Dynamical theory of X-ray diffraction A. Authier 12 The chemical bond in inorganic chemistry I. D. Brown 13 Structure determination from powder diffraction data W. I. F David, K. Shankland, L. B. McCusker, and Ch. Baerlocher, editors 14 Polymorphism in molecular crystals J. Bernstein

15 Crystallography of modular materials G. Ferraris, E. Makovicky, and S. Merlino 16 Diffuse x-ray scattering and models of disorder T. R. Welberry 17 Crystallography of the polymethylene chain: an inquiry into the structure of waxes D. L. Dorset 18 Crystalline molecular complexes and compounds: structure and principles F. H. Herbstein 19 Molecular aggregation: structure analysis and molecular simulation of crystals and liquids A. Gavezzotti 20 Aperiodic crystals: from modulated phases to quasicrystals T. Janssen, G. Chapuis, and M. de Boissieu 21 Incommensurate crystallography S. van Smaalen IUCr Texts on Crystallography 1 The solid state A. Guinier and R. Julien 4 X-ray charge densities and chemical bonding P. Coppens 5 The basics of crystallography and diffraction, second edition C. Hammond 6 Crystal structure analysis: principles and practice W. Clegg, editor 7 Fundamental of crystallography, second edition C. Giacovazza, editor 8 Crystal structure refinement: a crystallographer’s guide to SHELXL P. Müller, editor 9 Theories and techniques of crystal structure determination U. Shmueli 10 Advanced structural inorganic chemistry W.-K. Li, G.-D. Zhou, and T.C.W. Mak

Advanced Structural Inorganic Chemistry WAI-KEE LI The Chinese University of Hong Kong

GONG-DU ZHOU Peking University

THOMAS CHUNG WAI MAK The Chinese University of Hong Kong

1

3 Great Clarendon Street, Oxford OX2 6DP Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide in Oxford New York Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With offices in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Thailand Turkey Ukraine Vietnam Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries Published in the United States by Oxford University Press Inc., New York © Wai-Kee Li, Gong-Du Zhou and Thomas C.W. Mak The moral rights of the authors have been asserted Database right Oxford University Press (maker) First published 2008 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this book in any other binding or cover and you must impose this same condition on any acquirer British Library Cataloguing in Publication Data Data available Library of Congress Cataloging in Publication Data Data available Typeset by Newgen Imaging Systems (P) Ltd., Chennai, India Printed in Great Britain on acid-free paper by Biddles Ltd., King’s Lynn, Norfolk ISBN 978–0–19–921694–9 ISBN 978–0–19–921695–6 1 3 5 7 9 10 8 6 4 2

Preface The original edition of this book, written in Chinese for students in mainland China, was published in 2001 jointly by Chinese University Press and Peking University Press. The second edition was published by Peking University Press in 2006. During the preparation of the present English edition, we took the opportunity to correct some errors and to include updated material based on the recent literature. The book is derived from lecture notes used in various courses taught by the three authors at The Chinese University of Hong Kong and Peking University. The course titles include Chemical Bonding, Structural Chemistry, Structure and Properties of Matter, Advanced Inorganic Chemistry, Quantum Chemistry, Group Theory, and Chemical Crystallography. In total, the authors have accumulated over 100 man-years of teaching at the two universities. The book is designed as a text for senior undergraduates and beginning postgraduate students who need a deeper yet friendly exposure to the bonding and structure of chemical compounds. Structural chemistry is a branch of science that attempts to achieve a comprehensive understanding of the physical and chemical properties of various compounds from a microscopic viewpoint. In building up the theoretical framework, two main lines of development—electronic and spatial—are followed. In this book, both aspects and the interplay between them are stressed. It is hoped that our presentation will provide students with sufficient background and factual knowledge so that they can comprehend the exciting recent advances in chemical research and be motivated to pursue careers in universities and research institutes. This book is composed of three Parts. Part I, consisting of the first five chapters, reviews the basic theories of chemical bonding, beginning with a brief introduction to quantum mechanics, which is followed by successive chapters on atomic structure, bonding in molecules, and bonding in solids. Inclusion of the concluding chapter on computational chemistry reflects its increasing importance as an accessible and valuable tool in fundamental research. Part II of the book, again consisting of five chapters, discusses the symmetry concept and its importance in structural chemistry. Chapter 6 introduces students to symmetry point groups and the rudiments of group theory without delving into intricate mathematical details. Chapter 7 covers group theory’s most common chemical applications, including molecular orbital and hybridization theories, molecular vibrations, and selection rules. Chapter 8 utilizes the symmetry concept to discuss the bonding in coordination complexes. The final two

vi

Preface chapters address the formal description of symmetry in the crystalline state and the structures of basic inorganic crystals and some technologically important materials. Part III constitutes about half of the book. It offers a succinct description of the structural chemistry of the elements in the Periodic Table. Specifically, the maingroup elements (including noble gases) are covered in the first seven chapters, while the last three deal with the rare-earth elements, transition-metal clusters, and supramolecular systems, respectively. In all these chapters, selected examples illustrating interesting aspects of structure and bonding, generalizations of structural trends, and highlights from the recent literature are discussed in the light of the theoretical principles presented in Parts I and II. In writing the first two Parts, we deliberately avoided the use of rigorous mathematics in treating various theoretical topics. Instead, newly introduced concepts are illustrated with examples based on real chemical compounds or practical applications. Furthermore, in our selective compilation of material for presentation in Part III, we strive to make use of the most up-to-date crystallographic data to expound current research trends in structural inorganic chemistry. On the ground of hands-on experience, we freely make use of our own research results as examples in the presentation of relevant topics throughout the book. Certainly there is no implication whatsoever that they are particularly important or preferable to alternative choices. We faced a dilemma in choosing a fitting title for the book and eventually settled on the present one. The adjective “inorganic” is used in a broad sense as the book covers compounds of representative elements (including carbon) in the Periodic Table, organometallics, metal–metal bonded systems, coordination polymers, host–guest compounds and supramolecular assemblies. Our endeavor attempts to convey the message that inorganic synthesis is inherently less organized than organic synthesis, and serendipitous discoveries are being made from time to time. Hopefully, discussion of bonding and structure on the basis of X-ray structural data will help to promote a better understanding of modern chemical crystallography among the general scientific community. Many people have contributed to the completion of this book. Our past and present colleagues at The Chinese University of Hong Kong and Peking University have helped us in various ways during our teaching careers. Additionally, generations of students have left their imprint in the lecture notes on which this book is based. Their inquisitive feedback and suggestions for improvement have proved to be invaluable. Of course, we are solely responsible for deficiencies and errors and would most appreciate receiving comments and criticisms from prospective readers. The publication of the original Chinese edition was financed by a special grant from Chinese University Press, to which we are greatly indebted. We dedicate this book to our mentors: S.M. Blinder, You-Qi Tang, James Trotter and the late Hson-Mou Chang. Last but not least, we express our gratitude to

Preface

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our wives, Oi-Ching Chong Li, Zhi-Fen Liu, and Gloria Sau-Hing Mak, for their sacrifice, encouragement and unflinching support. Wai-Kee Li The Chinese University of Hong Kong Gong-Du Zhou Peking University Thomas Chung Wai Mak The Chinese University of Hong Kong

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Contents List of Contributors Part I

1

Fundamentals of Bonding Theory

1

Introduction to Quantum Theory

3 4 5 6 10 13 13 17 21 23 28

1.1 1.2 1.3 1.4 1.5

Dual nature of light and matter Uncertainty principle and probability concept Electronic wavefunction and probability density function Electronic wave equation: the Schrödinger equation Simple applications of the Schrödinger equation 1.5.1 Particle in a one-dimensional box 1.5.2 Particle in a three-dimensional box 1.5.3 Particle in a ring 1.5.4 Particle in a triangle References

2

xxi

The Electronic Structure of Atoms 2.1

The Hydrogen Atom 2.1.1 Schrödinger equation for the hydrogen atom 2.1.2 Angular functions of the hydrogen atom 2.1.3 Radial functions and total wavefunctions of the hydrogen atom 2.1.4 Relative sizes of hydrogenic orbitals and the probability criterion 2.1.5 Energy levels of hydrogenic orbitals; summary 2.2 The helium atom and the Pauli exclusion principle 2.2.1 The helium atom: ground state 2.2.2 Determinantal wavefunction and the Pauli Exclusion Principle 2.2.3 The helium atom: the 1s1 2s1 configuration 2.3 Many-electron atoms: electronic configuration and spectroscopic terms 2.3.1 Many-electron atoms 2.3.2 Ground electronic configuration for many-electron atoms 2.3.3 Spectroscopic terms arising from a given electronic configuration 2.3.4 Hund’s rules on spectroscopic terms 2.3.5 j–j Coupling 2.4 Atomic properties 2.4.1 Ionization energy and electron affinity

29 29 29 31 34 38 42 42 43 48 51 54 54 55 56 60 62 64 64

x

Contents 2.4.2 2.4.3 References

3

Electronegativity: the spectroscopic scale Relativistic effects on the properties of the elements

Covalent Bonding in Molecules The hydrogen molecular ion: bonding and antibonding molecular orbitals 3.1.1 The variational method 3.1.2 The hydrogen molecular ion: energy consideration 3.1.3 The hydrogen molecular ion: wavefunctions 3.1.4 Essentials of molecular orbital theory 3.2 The hydrogen molecule: molecular orbital and valence bond treatments 3.2.1 Molecular orbital theory for H2 3.2.2 Valence bond treatment of H2 3.2.3 Equivalence of the molecular orbital and valence bond models 3.3 Diatomic molecules 3.3.1 Homonuclear diatomic molecules 3.3.2 Heteronuclear diatomic molecules 3.4 Linear triatomic molecules and spn hybridization schemes 3.4.1 Beryllium hydride, BeH2 3.4.2 Hybridization scheme for linear triatomic molecules 3.4.3 Carbon dioxide, CO2 3.4.4 The spn (n = 1–3) hybrid orbitals 3.4.5 Covalent radii 3.5 Hückel molecular orbital theory for conjugated polyenes 3.5.1 Hückel molecular orbital theory and its application to ethylene and butadiene 3.5.2 Predicting the course of a reaction by considering the symmetry of the wavefunction References

67 71 76

77

3.1

4

Chemical Bonding in Condensed Phases 4.1 4.2

4.3

Chemical classification of solids Ionic bond 4.2.1 Ionic size: crystal radii of ions 4.2.2 Lattice energies of ionic compounds 4.2.3 Ionic liquids Metallic bonding and band theory 4.3.1 Chemical approach based on molecular orbital theory 4.3.2 Semiconductors 4.3.3 Variation of structure types of 4d and 5d transition metals 4.3.4 Metallic radii 4.3.5 Melting and boiling points and standard enthalpies of atomization of the metallic elements

77 77 79 82 84 85 85 86 89 91 92 96 99 99 100 101 104 109 110 110 113 116

118 118 121 121 124 126 128 128 130 131 132 133

Contents

5

xi

4.4

Van der Waals interactions 4.4.1 Physical origins of van der Waals interactions 4.4.2 Intermolecular potentials and van der Waals radii References

134 135 138 139

Computational Chemistry

140 140 141 142 142 143 143 144 145 146

5.1 5.2 5.3

Introduction Semi-empirical and ab initio methods Basis sets 5.3.1 Minimal basis set 5.3.2 Double zeta and split valence basis sets 5.3.3 Polarization functions and diffuse functions 5.4 Electron correlation 5.4.1 Configuration interaction 5.4.2 Perturbation methods 5.4.3 Coupled-cluster and quadratic configuration interaction methods 5.5 Density functional theory 5.6 Performance of theoretical methods 5.7 Composite methods 5.8 Illustrative examples 5.8.1 A stable argon compound: HArF 5.8.2 An all-metal aromatic species: Al2− 4 5.8.3 A novel pentanitrogen cation: N+ 5 5.8.4 Linear triatomics with noble gas–metal bonds 5.9 Software packages References

Part II

6

Symmetry in Chemistry

Symmetry and Elements of Group Theory 6.1

Symmetry elements and symmetry operations 6.1.1 Proper rotation axis Cn 6.1.2 Symmetry plane σ 6.1.3 Inversion center i 6.1.4 Improper rotation axis Sn 6.1.5 Identity element E 6.2 Molecular point groups 6.2.1 Classification of point groups 6.2.2 Identifying point groups 6.2.3 Dipole moment and optical activity 6.3 Character tables 6.4 The direct product and its use 6.4.1 The direct product 6.4.2 Identifying non-zero integrals and selection rules in spectroscopy 6.4.3 Molecular term symbols References Appendix 6.1 Character tables of point groups

146 147 148 151 152 152 154 156 158 162 163

165 167 167 167 168 169 169 170 170 170 178 179 180 185 185 187 189 193 195

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Contents

7

Application of Group Theory to Molecular Systems 7.1

Molecular orbital theory 7.1.1 AHn (n = 2–6) molecules 7.1.2 Hückel theory for cyclic conjugated polyenes 7.1.3 Cyclic systems involving d orbitals 7.1.4 Linear combinations of ligand orbitals for AL4 molecules with Td symmetry 7.2 Construction of hybrid orbitals 7.2.1 Hybridization schemes 7.2.2 Relationship between the coefficient matrices for the hybrid and molecular orbital wavefunctions 7.2.3 Hybrids with d-orbital participation 7.3 Molecular vibrations 7.3.1 The symmetries and activities of the normal modes 7.3.2 Some illustrative examples 7.3.3 CO stretch in metal carbonyl complexes 7.3.4 Linear molecules 7.3.5 Benzene and related molecules References

8

Bonding in Coordination Compounds Crystal field theory: d-orbital splitting in octahedral and tetrahedral complexes 8.2 Spectrochemical series, high spin and low spin complexes 8.3 Jahn–Teller distortion and other crystal fields 8.4 Octahedral crystal field splitting of spectroscopic terms 8.5 Energy level diagrams for octahedral complexes 8.5.1 Orgel diagrams 8.5.2 Intensities and band widths of d–d spectral lines 8.5.3 Tanabe–Sugano diagrams 8.5.4 Electronic spectra of selected metal complexes 8.6 Correlation of weak and strong field approximations 8.7 Spin–orbit interaction in complexes: the double group 8.8 Molecular orbital theory for octahedral complexes 8.8.1 σ bonding in octahedral complexes 8.8.2 Octahedral complexes with π bonding 8.8.3 The eighteen-electron rule 8.9 Electronic spectra of square planar complexes 8.9.1 Energy level scheme for square-planar complexes 8.9.2 Electronic spectra of square-planar halides and cyanides 8.10 Vibronic interaction in transition metal complexes 8.11 The 4f orbitals and their crystal field splitting patterns 8.11.1 The shapes of the 4f orbitals 8.11.2 Crystal field splitting patterns of the 4f orbitals References

213 213 214 221 227 228 232 232 233 234 236 236 239 246 252 254 259

261

8.1

261 263 265 267 268 268 271 274 274 279 280 282 283 285 288 289 289 291 294 295 295 297 298

Contents

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9

300 300 300 301 301 303 304 307 307 307 309 309 310 312 312 313 316 316 317 320 323 323 323 323 325

Symmetry in Crystals 9.1

The crystal as a geometrical entity 9.1.1 Interfacial angles 9.1.2 Miller indices 9.1.3 Thirty-two crystal classes (crystallographic point groups) 9.1.4 Stereographic projection 9.1.5 Acentric crystalline materials 9.2 The crystal as a lattice 9.2.1 The lattice concept 9.2.2 Unit cell 9.2.3 Fourteen Bravais lattices 9.2.4 Seven crystal systems 9.2.5 Unit cell transformation 9.3 Space groups 9.3.1 Screw axes and glide planes 9.3.2 Graphic symbols for symmetry elements 9.3.3 Hermann–Mauguin space–group symbols 9.3.4 International Tables for Crystallography 9.3.5 Coordinates of equipoints 9.3.6 Space group diagrams 9.3.7 Information on some commonly occurring space groups 9.3.8 Using the International Tables 9.4 Determination of space groups 9.4.1 Friedel’s law 9.4.2 Laue classes 9.4.3 Deduction of lattice centering and translational symmetry elements from systemic absences 9.5 Selected space groups and examples of crystal structures 9.5.1 Molecular symmetry and site symmetry 9.5.2 Symmetry deductions: assignment of atoms and groups to equivalent positions 9.5.3 Racemic crystal and conglomerate 9.5.4 Occurrence of space groups in crystals 9.6 Application of space group symmetry in crystal structure determination 9.6.1 Triclinic and monoclinic space groups 9.6.2 Orthorhombic space groups 9.6.3 Tetragonal space groups 9.6.4 Trigonal and rhombohedral space groups 9.6.5 Hexagonal space groups 9.6.6 Cubic space groups References

10 Basic Inorganic Crystal Structures and Materials 10.1 Cubic closest packing and related structures 10.1.1 Cubic closest packing (ccp)

328 333 333 333 338 338 339 340 343 345 347 350 353 362

364 364 364

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Contents 10.1.2 Structure of NaCl and related compounds 10.1.3 Structure of CaF2 and related compounds 10.1.4 Structure of cubic zinc sulfide 10.1.5 Structure of spinel and related compounds 10.2 Hexagonal closest packing and related structures 10.2.1 Hexagonal closest packing (hcp) 10.2.2 Structure of hexagonal zinc sulfide 10.2.3 Structure of NiAs and related compounds 10.2.4 Structure of CdI2 and related compounds 10.2.5 Structure of α-Al2 O3 10.2.6 Structure of rutile 10.3 Body-centered cubic packing and related structures 10.3.1 Body-centered cubic packing (bcp) 10.3.2 Structure and properties of α-AgI 10.3.3 Structure of CsCl and related compounds 10.4 Perovskite and related compounds 10.4.1 Structure of perovskite 10.4.2 Crystal structure of BaTiO3 10.4.3 Superconductors of perovskite structure type 10.4.4 ReO3 and related compounds 10.5 Hard magnetic materials 10.5.1 Survey of magnetic materials 10.5.2 Structure of SmCo5 and Sm2 Co17 10.5.3 Structure of Nd2 Fe14 B References

366 370 371 373 375 375 376 376 377 379 380 381 381 383 384 385 385 388 389 390 391 391 393 393 395

Part III Structural Chemistry of Selected Elements

397

11 Structural Chemistry of Hydrogen

399 399 403 403 405 406 408 409 411 411 412 413 415 416 417 419

11.1 The bonding types of hydrogen 11.2 Hydrogen bond 11.2.1 Nature and geometry of the hydrogen bond 11.2.2 The strength of hydrogen bonds 11.2.3 Symmetrical hydrogen bond 11.2.4 Hydrogen bonds in organometallic compounds 11.2.5 The universality and importance of hydrogen bonds 11.3 Non-conventional hydrogen bonds 11.3.1 X–H· · · π hydrogen bond 11.3.2 Transition metal hydrogen bond X–H· · · M 11.3.3 Dihydrogen bond X–H· · · H–E 11.3.4 Inverse hydrogen bond 11.4 Hydride complexes 11.4.1 Covalent metal hydride complexes 11.4.2 Interstitial and high-coordinate hydride complexes 11.5 Molecular hydrogen (H2 ) coordination compounds and σ -bond complexes 11.5.1 Structure and bonding of H2 coordination compounds 11.5.2 X–H σ -bond coordination metal complexes

422 422 424

Contents 11.5.3 Agostic bond 11.5.4 Structure and bonding of σ complexes References

12 Structural Chemistry of Alkali and Alkaline-Earth Metals 12.1 Survey of the alkali metals 12.2 Structure and bonding in inorganic alkali metal compounds 12.2.1 Alkali metal oxides 12.2.2 Lithium nitride 12.2.3 Inorganic alkali metal complexes 12.3 Structure and bonding in organic alkali metal compounds 12.3.1 Methyllithium and related compounds 12.3.2 π -Complexes of lithium 12.3.3 π -Complexes of sodium and potassium 12.4 Alkalides and electrides 12.4.1 Alkalides 12.4.2 Electrides 12.5 Survey of the alkaline-earth metals 12.6 Structure of compounds of alkaline-earth metals 12.6.1 Group 2 metal complexes 12.6.2 Group 2 metal nitrides 12.6.3 Group 2 low-valent oxides and nitrides 12.7 Organometallic compounds of group 2 elements 12.7.1 Polymeric chains 12.7.2 Grignard reagents 12.7.3 Alkaline-earth metallocenes 12.8 Alkali and alkaline-earth metal complexes with inverse crown structures References

13 Structural Chemistry of Group 13 Elements 13.1 Survey of the group 13 elements 13.2 Elemental Boron 13.3 Borides 13.3.1 Metal borides 13.3.2 Non-metal borides 13.4 Boranes and carboranes 13.4.1 Molecular structure and bonding 13.4.2 Bond valence in molecular skeletons 13.4.3 Wade’s rules 13.4.4 Chemical bonding in closo-boranes 13.4.5 Chemical bonding in nido- and arachno-boranes 13.4.6 Electron-counting scheme for macropolyhedral boranes: mno rule 13.4.7 Electronic structure of β-rhombohedral boron 13.4.8 Persubstituted derivatives of icosahedral borane B12 H2− 12 13.4.9 Boranes and carboranes as ligands

xv 425 428 430

432 432 433 433 435 436 442 442 443 445 446 446 447 449 450 450 451 452 454 454 454 455 456 458 460 460 461 464 464 467 470 470 472 473 475 477 479 481 482 483

xvi

Contents 13.4.10 Carborane skeletons beyond the icosahedron 13.5 Boric acid and borates 13.5.1 Boric acid 13.5.2 Structure of borates 13.6 Organometallic compounds of group 13 elements 13.6.1 Compounds with bridged structure 13.6.2 Compounds with π bonding 13.6.3 Compounds containing M–M bonds 13.6.4 Linear catenation in heavier group 13 elements 13.7 Structure of naked anionic metalloid clusters 13.7.1 Structure of Ga84 [N(SiMe3 )2 ]4− 20 13.7.2 Structure of NaTl 13.7.3 Naked Tlm− n anion clusters References

485 486 486 487 490 490 491 492 494 494 495 495 496 498

14 Structural Chemistry of Group 14 Elements

500 500 500 501 502 506 507 509 509 510 511 517 517 520 520 520 524 527 529 533 533 534 535 540 544 544 546 547 549 549 550

14.1 Allotropic modifications of carbon 14.1.1 Diamond 14.1.2 Graphite 14.1.3 Fullerenes 14.1.4 Amorphous carbon 14.1.5 Carbon nanotubes 14.2 Compounds of carbon 14.2.1 Aliphatic compounds 14.2.2 Aromatic compounds 14.2.3 Fullerenic compounds 14.3 Bonding in carbon compounds 14.3.1 Types of bonds formed by the carbon atom 14.3.2 Coordination numbers of carbon 14.3.3 Bond lengths of C–C and C–X bonds 14.3.4 Factors influencing bond lengths 14.3.5 Abnormal carbon–carbon single bonds 14.3.6 Complexes containing a naked carbon atom 14.3.7 Complexes containing naked dicarbon ligands 14.4 Structural chemistry of silicon 14.4.1 Comparison of silicon and carbon 14.4.2 Metal silicides 14.4.3 Stereochemistry of silicon 14.4.4 Silicates 14.5 Structures of halides and oxides of heavier group 14 elements 14.5.1 Subvalent halides 14.5.2 Oxides of Ge, Sn, and Pb 14.6 Polyatomic anions of Ge, Sn, and Pb 14.7 Organometallic compounds of heavier group 14 elements 14.7.1 Cyclopentadienyl complexes 14.7.2 Sila- and germa-aromatic compounds

Contents 14.7.3 Cluster complexes of Ge, Sn, and Pb 14.7.4 Metalloid clusters of Sn 14.7.5 Donor–acceptor complexes of Ge, Sn and Pb References

15 Structural Chemistry of Group 15 Elements 15.1 The N2 molecule, all-nitrogen ions and dinitrogen complexes 15.1.1 The N2 molecule 15.1.2 Nitrogen ions and catenation of nitrogen 15.1.3 Dinitrogen complexes 15.2 Compounds of nitrogen 15.2.1 Molecular nitrogen oxides 15.2.2 Oxo-acids and oxo-ions of nitrogen 15.2.3 Nitrogen hydrides 15.3 Structure and bonding of elemental phosphorus and Pn groups 15.3.1 Elemental phosphorus 15.3.2 Polyphosphide anions 15.3.3 Structure of Pn groups in transition-metal complexes 15.3.4 Bond valence in Pn species 15.4 Bonding type and coordination geometry of phosphorus 15.4.1 Potential bonding types of phosphorus 15.4.2 Coordination geometries of phosphorus 15.5 Structure and bonding in phosphorus–nitrogen and phosphorus–carbon compounds 15.5.1 Types of P–N bonds 15.5.2 Phosphazanes 15.5.3 Phosphazenes 15.5.4 Bonding types in phosphorus–carbon compounds 15.5.5 π -Coordination complexes of phosphorus–carbon compounds 15.6 Structural chemistry of As, Sb, and Bi 15.6.1 Stereochemistry of As, Sb, and Bi 15.6.2 Metal–metal bonds and clusters 15.6.3 Intermolecular interactions in organoantimony and organobismuth compounds References

16 Structural Chemistry of Group 16 Elements 16.1 Dioxygen and ozone 16.1.1 Structure and properties of dioxygen 16.1.2 Crystalline phases of solid oxygen 16.1.3 Dioxygen-related species and hydrogen peroxide 16.1.4 Ozone 16.2 Oxygen and dioxygen metal complexes 16.2.1 Coordination modes of oxygen in metal–oxo complexes 16.2.2 Ligation modes of dioxygen in metal complexes 16.2.3 Biological dioxygen carriers

xvii 551 553 554 557 561 561 561 561 564 569 569 575 578 579 579 581 581 584 586 586 587 590 590 591 593 596 600 602 602 605 607 608 610 610 610 612 613 614 616 616 616 618

xviii

Contents 16.3 Structure of water and ices 16.3.1 Water in the gas phase 16.3.2 Water in the solid phase: ices 16.3.3 Structural model of liquid water 16.3.4 Protonated water species, H3 O+ and H5 O+ 2 16.4 Allotropes of sulfur and polyatomic sulfur species 16.4.1 Allotropes of sulfur 16.4.2 Polyatomic sulfur ions 16.5 Sulfide anions as ligands in metal complexes 16.5.1 Monosulfide S2− 16.5.2 Disulfide S2− 2

16.5.3 Polysulfides S2− n 16.6 Oxides and oxoacids of sulfur 16.6.1 Oxides of sulfur 16.6.2 Oxoacids of sulfur 16.7 Sulfur–nitrogen compounds 16.7.1 Tetrasulfur tetranitride, S4 N4 16.7.2 S2 N2 and (SN)x 16.7.3 Cyclic sulfur–nitrogen compounds 16.8 Structural chemistry of selenium and tellurium 16.8.1 Allotropes of selenium and tellurium 16.8.2 Polyatomic cations and anions of selenium and tellurium 16.8.3 Stereochemistry of selenium and tellurium References

17 Structural Chemistry of Group 17 and Group 18 Elements 17.1 Elemental halogens 17.1.1 Crystal structures of the elemental halogens 17.1.2 Homopolyatomic halogen anions 17.1.3 Homopolyatomic halogen cations 17.2 Interhalogen compounds and ions 17.2.1 Neutral interhalogen compounds 17.2.2 Interhalogen ions 17.3 Charge-transfer complexes of halogens 17.4 Halogen oxides and oxo compounds 17.4.1 Binary halogen oxides 17.4.2 Ternary halogen oxides 17.4.3 Halogen oxoacids and anions 17.4.4 Structural features of polycoordinate iodine compounds 17.5 Structural chemistry of noble gas compounds 17.5.1 General survey 17.5.2 Stereochemistry of xenon 17.5.3 Chemical bonding in xenon f luorides 17.5.4 Structures of some inorganic xenon compounds 17.5.5 Structures of some organoxenon compounds

619 620 620 623 627 627 626 630 631 631 632 632 634 634 637 641 641 642 643 644 644 644 649 652

654 654 654 654 656 657 657 659 660 662 662 664 666 668 670 670 671 672 674 677

Contents 17.5.6 Gold–xenon complexes 17.5.7 Krypton compounds References

18 Structural Chemistry of Rare-Earth Elements 18.1 Chemistry of rare-earth metals 18.1.1 Trends in metallic and ionic radii: lanthanide contraction 18.1.2 Crystal structures of the rare-earth metals 18.1.3 Oxidation states 18.1.4 Term symbols and electronic spectroscopy 18.1.5 Magnetic properties 18.2 Structure of oxides and halides of rare-earth elements 18.2.1 Oxides 18.2.2 Halides 18.3 Coordination geometry of rare-earth cations 18.4 Organometallic compounds of rare-earth elements 18.4.1 Cyclopentadienyl rare-earth complexes 18.4.2 Biscyclopentadienyl complexes 18.4.3 Benzene and cyclooctatetraenyl rare-earth complexes 18.4.4 Rare-earth complexes with other organic ligands 18.5 Reduction chemistry in oxidation state +2 18.5.1 Samarium(II) iodide 18.5.2 Decamethylsamarocene References

19 Metal–Metal Bonds and Transition-Metal Clusters 19.1 Bond valence and bond number of transition-metal clusters 19.2 Dinuclear complexes containing metal–metal bonds 19.2.1 Dinuclear transition-metal complexes conforming to the 18-electron rule 19.2.2 Quadruple bonds 19.2.3 Bond valence of metal–metal bond 19.2.4 Quintuple bonding in a dimetal complex 19.3 Clusters with three or four transition-metal atoms 19.3.1 Trinuclear clusters 19.3.2 Tetranuclear clusters 19.4 Clusters with more than four transition-metal atoms 19.4.1 Pentanuclear clusters 19.4.2 Hexanuclear clusters 19.4.3 Clusters with seven or more transition-metal atoms 19.4.4 Anionic carbonyl clusters with interstitial main-group atoms 19.5 Iso-bond valence and iso-structural series 19.6 Selected topics in metal–metal interactions 19.6.1 Aurophilicity 19.6.2 Argentophilicity and mixed metal complexes

xix 678 679 680

682 682 682 683 684 685 687 688 688 689 690 694 694 696 697 697 699 699 700 701

703 703 705 707 708 711 712 713 713 714 715 715 715 717 718 719 721 721 724

xx

Contents 19.6.3 Metal string molecules 19.6.4 Metal-based infinite chains and networks References

20 Supramolecular Structural Chemistry 20.1 Introduction 20.1.1 Intermolecular interactions 20.1.2 Molecular recognition 20.1.3 Self-assembly 20.1.4 Crystal engineering 20.1.5 Supramolecular synthon 20.2 Hydrogen-bond directed assembly 20.2.1 Supramolecular architectures based on the carboxylic acid dimer synthon 20.2.2 Graph-set encoding of hydrogen-bonding pattern 20.2.3 Supramolecular construction based on complementary hydrogen bonding between heterocycles 20.2.4 Hydrogen-bonded networks exhibiting the supramolecular rosette pattern 20.3 Supramolecular chemistry of the coordination bond 20.3.1 Principal types of supermolecules 20.3.2 Some examples of inorganic supermolecules 20.3.3 Synthetic strategies for inorganic supermolecules and coordination polymers 20.3.4 Molecular polygons and tubes 20.3.5 Molecular polyhedra 20.4 Selected examples in crystal engineering 20.4.1 Diamondoid networks 20.4.2 Interlocked structures constructed from cucurbituril 20.4.3 Inorganic crystal engineering using hydrogen bonds 20.4.4 Generation and stabilization of unstable inorganic/organic anions in urea/thiourea complexes 20.4.5 Supramolecular assembly of silver(I) polyhedra with embedded acetylenediide dianion 20.4.6 Supramolecular assembly with the silver(I)-ethynide synthon 20.4.7 Self-assembly of nanocapsules with pyrogallol[4]arene macrocycles 20.4.8 Reticular design and synthesis of porous metal–organic frameworks 20.4.9 One-pot synthesis of nanocontainer molecule 20.4.10 Filled carbon nanotubes References

Index

724 729 731 733 733 733 734 735 735 737 738 740 742 744 744 752 752 753 757 760 762 768 768 772 776 780 784 792 797 799 804 804 808 811

List of Contributors Wai-Kee Li obtained his B.S. degree from University of Illinois in 1964 and his Ph.D. degree from University of Michigan in 1968. He joined the Chinese University of Hong Kong in July 1968 to follow an academic career that spanned a period of thirty-eight years. He retired as Professor of Chemistry in August 2006 and was subsequently conferred the title of Emeritus Professor of Chemistry. Over the years he taught a variety of courses in physical and inorganic chemistry. His research interests in theoretical and computational chemistry have led to over 180 papers in international journals. Gong-Du Zhou graduated from Xichuan University in 1953 and completed his postgraduate studies at Peking University in 1957. He then joined the Chemistry Department of Peking University and taught Structural Chemistry, Structure and Properties of Matter, and other courses there till his retirement as a Professor in 1992. He has published more than 100 research papers in X-ray crystallography and structural chemistry, together with over a dozen Chinese chemistry textbooks and reference books. Thomas Chung Wai Mak obtained his B.Sc. (1960) and Ph.D. (1963) degrees from the University of British Columbia. After working as a NASA Postdoctoral Research Associate at the University of Pittsburgh and an Assistant Professor at the University of Western Ontario, in June 1969 he joined the Chinese University of Hong Kong, where he is now Emeritus Professor of Chemistry and Wei Lun Research Professor. His research interest lies in inorganic synthesis, chemical crystallography, supramolecular assembly and crystal engineering, with over 900 papers in international journals. He was elected as a member of the Chinese Academy of Sciences in 2001.

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Fundamentals of Bonding Theory

The theory of chemical bonding plays an important role in the rapidly evolving field of structural inorganic chemistry. It helps us to understand the structure, physical properties and reactivities of different classes of compounds. It is generally recognized that bonding theory acts as a guiding principle in inorganic chemistry research, including the design of synthetic schemes, rationalization of reaction mechanisms, exploration of structure–property relationships, supramolecular assembly and crystal engineering. There are five chapters in Part I: Introduction to quantum theory, The electronic structure of atoms, Covalent bonding in molecules, Chemical bonding in condensed phases and Computational chemistry. Since most of the contents of these chapters are covered in popular texts for courses in physical chemistry, quantum chemistry and structural chemistry, it can be safely assumed that readers of this book have some acquaintance with such topics. Consequently, many sections may be viewed as convenient summaries and frequently mathematical formulas are given without derivation. The main purpose of Part I is to review the rudiments of bonding theory, so that the basic principles can be applied to the development of new topics in subsequent chapters.

I

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Introduction to Quantum Theory

In order to appreciate fully the theoretical basis of atomic structure and chemical bonding, we need a basic understanding of the quantum theory. Even though chemistry is an experimental science, theoretical consideration (especially prediction) is now playing a role of increasing importance with the development of powerful computational algorithms. The field of applying quantum theoretical methods to investigate chemical systems is commonly called quantum chemistry. The key to theoretical chemistry is molecular quantum mechanics, which deals with the transference or transformation of energy on a molecular scale. Although the quantum mechanical principles for understanding the electronic structure of matter has been recognized since 1930, the mathematics involved in their application, i.e. general solution of the Schrödinger equation for a molecular system, was intractable at best in the 50 years or so that followed. But with the steady development of new theoretical and computational methods, as well as the availability of larger and faster computers with reasonable price tags during the past two decades, calculations have sometimes become almost as accurate as experiments, or at least accurate enough to be useful to experimentalists. Additionally, compared to experiments, calculations are often less costly, less time-consuming, and easier to control. As a result, computational results can complement experimental studies in essentially every field of chemistry. For instance, in physical chemistry, chemists can apply quantum chemical methods to calculate the entropy, enthalpy, and other thermochemical functions of various gases, to interpret molecular spectra, to understand the nature of the intermolecular forces, etc. In organic chemistry, calculations can serve as a guide to a chemist who is in the process of synthesizing or designing new compounds; they can also be used to compare the relative stabilities of various molecular species, to study the properties of reaction intermediates and transition states, and to investigate the mechanism of reactions, etc. In analytical chemistry, theory can help chemists to understand the frequencies and intensities of the spectral lines. In inorganic chemistry, chemists can apply the ligand filed theory to study the transition metal complexes. An indication that computational chemistry has been receiving increasing attention in the scientific community was the award of the 1998 Nobel Prize in chemistry to Professor J.A. Pople and Professor W. Kohn for their contributions to quantum chemistry. In Chapter 5, we will briefly describe the kind of questions that may be fruitfully treated by computational chemistry.

1

4

Fundamentals of Bonding Theory In this chapter, we discuss some important concepts of quantum theory. A clear understanding of these concepts will facilitate subsequent discussion of bonding theory.

1.1

Dual nature of light and matter

Around the beginning of the twentieth century, scientists had accepted that light is both a particle and a wave. The wave character of light is manifested in its interference and diffraction experiments. On the other hand, its corpuscular nature can be seen in experiments such as the photoelectric effect and Compton effect. With this background, L. de Broglie in 1924 proposed that, if light is both a particle and a wave, a similar duality also exists for matter. Moreover, by combining Einstein’s relationship between energy E and mass m, E = mc2 ,

(1.1.1)

where c is the speed of light, and Planck’s quantum condition, E = hν,

(1.1.2)

where h is Planck’s constant and ν is the frequency of the radiation, de Broglie was able to arrive at the wavelength λ associated with a photon, λ=

h hc hc h c = = = = , ν hν mc p mc2

(1.1.3)

where p is the momentum of the photon. Then de Broglie went on to suggest that a particle with mass m and velocity v is also associated with a wavelength given by λ=

h h = , mv p

(1.1.4)

where p is now the momentum of the particle. Before proceeding further, it is instructive to examine what kinds of wavelengths are associated with particles having various masses and velocities, as shown in Table 1.1.1. By examining the results listed in Table 1.1.1, it is seen that the wavelengths of macroscopic objects will be far too short to be observed. On the other hand, electrons with energies on the order of 100 eV will have wavelengths between 100 and 200 pm, approximately the interatomic distances in crystals. In 1927, C.J. Davisson and L.H. Germer obtained the first electron diffraction pattern of a crystal, thus proving de Broglie’s hypothesis experimentally. From then on, scientists recognized that an electron has dual properties: it can behave as both a particle and a wave.

Introduction to Quantum Theory Table 1.1.1. Wavelength of different particles travelling with various velocities (λ = h/p = h/mv; h = 6.63 × 10−27 erg s = 6.63 × 10−34 J s)

Particles

m / kg

v / m s−1

λ / pm

Electron at 298 K 1-volt electron 100-volt electron He atom at 298 K Xe atom at 298 K A 100-kg sprinter running at worldrecord speed

9.11 × 10−31 9.11 × 10−31 9.11 × 10−31 6.65 × 10−27 2.18 × 10−25 1.00 × 102

1.16 × 105 5.93 × 105 5.93 × 106 1.36 × 103 2.38 × 102 1.00 × 101

6270∗ 1230 123† 73.3 12.8 6.63 × 10−25

"1

"1

−23 J K −1 ×298 K 2 3kT 2 = 3×1.38×10 = 1.16 × 105 m 9.11×10−31 kg h 6.63×10−34 Js −9 λ = mv = 9.11×10−31 kg×1.16×105 m s−1 = 6.27 × 10 m = 6270 pm. † E = 100 eV = 100 × 1.60 × 10−19 J = 1.60 × 10−17 J = 1 mv 2 , 2

∗E

= 32 kT = 12 mv 2 ; v =

v=

λ=

"1

!

!

"1

−17 J 2 2E 2 = 2×1.60×10 = 5.93 × 106 m s−1 ; m 9.11×10−31 kg −34 h 6.63×10 Js −10 m mv = 9.11×10−31 kg×5.93×106 m s−1 = 1.23 × 10

!

!

m s−1 ;

= 123 pm.

This wavelength is similar to the atomic spacing in crystals.

1.2

Uncertainty principle and probability Concept

Another important development in quantum mechanics is the Uncertainty Principle set forth by W. Heisenberg in 1927. In its simplest terms, this principle says, “The position and momentum of a particle cannot be simultaneously and precisely determined.” Quantitatively, the product of the uncertainty in the x component of the momentum vector ('px ) and the uncertainty in the x direction of the particle’s position ('x) is on the order of Planck’s constant: ('px )('x) ∼

h = 5.27 × 10−35 J s. 4π

(1.2.1)

While h is quite small in the macroscopic world, it is not at all insignificant when the particle under consideration is of subatomic scale. Let us use an actual example to illustrate this point. Suppose the 'x of an electron is 10−14 m, or 0.01 pm. Then, with eq. (1.2.1), we get 'px = 5.27 × 10−21 kg m s−1 . This uncertainty in momentum would be quite small in the macroscopic world. However, for subatomic particles such as an electron, with mass of 9.11×10−31 kg, such an uncertainty would not be negligible at all. Hence, on the basis of the Uncertainty Principle, we can no longer say that an electron is precisely located at this point with an exactly known velocity. It should be stressed that the uncertainties we are discussing here have nothing to do with the imperfection of the measuring instruments. Rather, they are inherent indeterminacies. If we recall the Bohr theory of the hydrogen atom, we find that both the radius of the orbit and the velocity of the electron can be precisely calculated. Hence the Bohr results violate the Uncertainty Principle. With the acceptance of uncertainty at the atomic level, we are forced to speak in terms of probability: we say the probability of finding the electron within

5

6

Fundamentals of Bonding Theory this volume element is how many percent and it has a probable velocity (or momentum) such and such. 1.3

Electronic wavefunction and probability density function

Since an electron has wave character, we can describe its motion with a wave equation, as we do in classical mechanics for the motions of a water wave or a stretched string or a drum. If the system is one-dimensional, the classical wave equation is 1 ∂ 2 Φ(x, t) ∂ 2 Φ(x, t) = 2 , 2 ∂x v ∂t 2

(1.3.1)

where v is the velocity of the propagation. The wavefunction Φ gives the displacement of the wave at point x and at time t. In three-dimensional space, the wave equation becomes $ # 2 ∂2 ∂2 1 ∂ 2 Φ(x, y, z, t) ∂ 2 Φ(x, y, z, t) = ∇ + + Φ(x, y, z, t) = . ∂x2 ∂y2 ∂z 2 v2 ∂t 2 (1.3.2) A typical wavefunction, or a solution of the wave equation, is the familiar sine or cosine function. For example, we can have Φ(x, t) = A sin(2π/λ)(x − vt).

(1.3.3)

It can be easily verified that Φ(x, t) satisfies eq. (1.3.1). An important point to keep in mind is that, in classical mechanics, the wavefunction is an amplitude function. As we shall see later, in quantum mechanics, the electronic wavefunction has a different role to play. Combining the wave nature of matter and the probability concept of the Uncertainty Principle, M. Born proposed that the electronic wavefunction is no longer an amplitude function. Rather, it is a measure of the probability of an event: when the function has a large (absolute) value, the probability for the event is large. An example of such an event is given below. From the Uncertainty Principle, we no longer speak of the exact position of an electron. Instead, the electron position is defined by a probability density function. If this function is called ρ (x, y, z), then the electron is most likely found in the region where ρ has the greatest value. In fact, ρ dτ is the probability of finding the electron in the volume element dτ (≡ dxdydz) surrounding the point (x, y, z). Note that ρ has the unit of volume−1 , and ρ dτ , being a probability, is dimensionless. If we call the electronic wavefunction ψ, Born asserted that the probability density function ρ is simply the absolute square of ψ: ρ(x, y, z) = |ψ(x, y, z)|2 .

(1.3.4)

Introduction to Quantum Theory Since ψ can take on imaginary values, we take the absolute square of ψ to make sure that ρ is positive. Hence, when ψ is imaginary, ρ(x, y, z) = |ψ(x, y, z)|2 = ψ ∗ ψ,

(1.3.5)

where ψ ∗ is the complex conjugate (replacing i in ψ by –i) of ψ. Before proceeding further, let us use some numerical examples to illustrate the determination of the probability of locating an electron in a certain volume element in space. The ground state wavefunction of the hydrogen atom is "− 1 ! 2 − ar ψ1s = π a03 e 0,

(1.3.6)

where r is the nucleus–electron separation and a0 , with the value of 52.9 pm, is the radius of the first Bohr orbit (hence is called Bohr radius). In the following we will use ψ1s to determine the probability P of locating the electron in a volume element dr of 1 pm3 which is 1a0 away from the nucleus. At r = 1a0 , ! % "− 1 a0 &− 1 3 2 −a 2 −1 e 0 = π(52.9 pm)3 e = 5.39 × 10−4 pm− 2 , ψ1s = π a03 " ! 3 2 ρ = |ψ1s |2 = 5.39 × 10−4 pm− 2 = 2.91 × 10−7 pm−3 ,

P = |ψ1s |2 dτ = 2.91 × 10−7 pm−3 × 1 pm3 = 2.91 × 10−7 . In addition, we can also calculate the probability of finding the electron in a shell of thickness 1 pm which is 1a0 away from the nucleus: dτ = (surface area) × (thickness)

= (4π r 2 dr) = 4π(52.9 pm)2 × 1 pm = 3.52 × 104 pm3 ,

and P = |ψ1s |2 dτ = 2.91 × 10−7 pm−3 × 3.52 × 104 pm3 = 1.02 × 10−2 . In other words, there is about 1% chance of finding the electron in a spherical shell of thickness 1 pm and radius 1a0 . In Table 1.3.1, we tabulate ψ1s , |ψ1s |2 , |ψ1s |2 dτ (with dτ = 1 pm3 ), and 4πr 2 |ψ1s |2 dr (with dr = 1 pm), for various r values. As |ψ|2 dτ represents the probability of finding the electron in a certain region in space, and the sum of all probabilities is 1, ψ must satisfy the relation ' |ψ|2 dτ = 1. (1.3.7)

7

8

Fundamentals of Bonding Theory Table 1.3.1. Values of ψ1s , |ψ1s |2 , |ψ1s |2 dτ (with dτ = 1 pm3 ), and 4πr 2 |ψ1s |2 dr (with dr = 1 pm) for various nucleus–electron distances

r(pm) # $ −3 ψ1s pm 2 ! " |ψ1s |2 pm−3 |ψ1s |2 dτ 4πr 2 |ψ1s |2 dr

0

26.45 (or a0 /2)

52.9 (or a0 )

100

200

1.47 × 10−3

8.89 × 10−4

5.39 × 10−4

2.21 × 10−4

3.34 × 10−5

2.15 × 10−6

7.91 × 10−7

2.91 × 10−7

4.90 ×10−8

1.12 ×10−9

0

6.95 ×10−3

1.02×10−2

6.16 ×10−3

2.15 ×10−6

7.91 ×10−7

2.91 ×10−7

4.90 ×10−8

1.12 ×10−9 5.62 ×10−4

When ψ satisfies eq. ( (1.3.7), the wavefunction is said to be normalized. On the other hand, if |ψ|2 dτ = N , where N is a constant, then N −1/2 ψ is a normalized wavefunction and N −1/2 is called the normalization constant. For a given system, there are often many or even an infinite number of acceptable solutions: ψ1 , ψ2 , . . . , ψi , ψj , . . . and these wavefunctions are “orthogonal” to each other, i.e. '

ψi∗ ψj dτ =

'

ψj∗ ψi dτ = 0.

(1.3.8)

Combining the normalization condition (eq. (1.3.7)) and the orthogonality condition (eq. (1.3.8)) leads us to the orthonormality relationship among the wavefunctions ' ' ∗ ψi ψj dτ = ψj∗ ψi dτ = δij =

)

0 1

when i ' = j , when i = j

(1.3.9)

where δij is the Kronecker delta function. Since |ψ|2 plays the role of a probability density function, ψ must be finite, continuous, and single-valued. The wavefunction plays a central role in quantum mechanics. For atomic systems, the wavefunction describing the electronic distribution is called an atomic orbital; in other words, the aforementioned 1s wavefunction of the ground state of a hydrogen atom is also called the 1s orbital. For molecular systems, the corresponding wavefunctions are likewise called molecular orbitals. Once we know the explicit functions of the various atomic orbitals (such as 1s, 2s, 2p, 3s, 3p, 3d,…), we can calculate the values of ψ at different points in space and express the wavefunction graphically. In Fig. 1.3.1(a), the graph on the left is a plot of ψ1s against r; the sphere on the right shows that ψ has the same value for a given r, regardless of direction (or θ and ϕ values). In Fig. 1.3.1(b), the two graphs on the left plot density functions |ψ1s |2 and 4πr 2 |ψ1s |2 against r. The probability density describing the electronic distribution is also referred to as an electron cloud, which may be represented by a figure such as that shown on the right side of Fig. 1.3.1(b). This figure indicates that the 1s orbital has maximum density at the nucleus and the density decreases steadily as the electron gets farther and farther away from the nucleus.

Introduction to Quantum Theory

9

z cls/10–4/pm–3/2

15 10

cls y

5 x 0

4πr2!cls!2/10–3/pm–1 !cls!2/10–6/pm–3

(a)

z

2 !cls!2 0

y rp

10

x

4πr2!cls!2

0

0

Fig. 1.3.1.

(a) The 1s wavefunction and (b) the 1s probability density functions of the hydrogen atom.

200

100

(b)

r /pm

In addition to providing probability density functions, the wavefunction may also be used to calculate the value of a physical observable for that state. In quantum mechanics, a physical observable A has a corresponding mathematical operator Â. When  satisfies the relation ˆ = aψ, Aψ

(1.3.10)

ψ is called an eigenfunction of operator Â, and a is called the eigenvalue of the state described by ψ. In the next section, we shall discuss the Schrödinger equation, Hˆ ψ = Eψ.

(1.3.11)

Here ψ is the eigenfunction of the Hamiltonian operator Hˆ and the corresponding eigenvalue E is the energy of the system. If ψ does not satisfy eq. (1.3.10), we can calculate the expectation value (or mean) of A, , by the expression (

= (

ˆ dτ ψ ∗ Aψ |ψ|2 dτ

.

(1.3.12)

If ψ is a normalized wavefunction, eq. (1.3.12) becomes =

'

ˆ dτ . ψ ∗ Aψ

(1.3.13)

10

Fundamentals of Bonding Theory In the ground state of a hydrogen atom, there is no fixed r value for the electron, i.e. there is no eigenvalue for r. On the other hand, we can use eq. (1.3.13) to calculate the average value of r: "−1 ' ! = πa03

2π 0

dφ

' "−1 ! 3 · 4π = πa0

'

∞ 0

π 0

e

sin θdθ

− a2r 3 0

'

0

∞

e

− ar

0

re

− ar

0

r 2 dr

r dr

= 3a0 /2.

(1.3.14)

In carrying out the integration in eq. (1.3.14), we make use of dτ = r 2 dr sin θ dθ dϕ and 0 ≤ r < ∞, 0 ≤ θ ≤ π, and 0 ≤ φ ≤ 2π . In Fig. 1.3.1(b), in the plot of 4π r 2 |ψ1s |2 against r, the mean value is marked on the r axis, separating the graph into two parts. These two parts have unequal areas, the unshaded area being larger than the shaded area. This result implies that it is more likely to find a r value smaller than than one larger than . In addition, the r value corresponding to the maximum in the 4πr 2 |ψ1s |2 function is labelled rp . At rp , r = a0 and rp is called the most probable electron distance. 1.4

Electronic wave equation: The Schrödinger equation

In 1926, E. Schrödinger developed his famous wave equation for electrons. The validity of the Schrödinger equation rests solely on the fact that it leads to the right answers for a variety of systems. As in the case of Newton’s equations, the Schrödinger equation is a fundamental postulate that cannot be deduced from first principles. Hence what is presented below is merely a heuristic derivation. In this presentation, we can see how the particle character is incorporated into a wave equation. We start with eq. (1.3.2), the general differential equation for wave motion: ∇ 2 Φ(x, y, z, t) =

∂ 2 Φ(x, y, z, t) . v 2 ∂t 2

(1.3.2)

Note that wavefunction Φ has time t as one of its variables. Since our primary concern is the energy of a system and this energy is independent of time (we are ignoring the process of radiation here), we need an equation that is time independent. The wavefunctions obtained from a time-independent equation are called standing (or stationary) waves. To obtain such an equation, we assume Φ(x, y, z, t) has the form Φ(x, y, z, t) = ψ(x, y, z)g(t),

(1.4.1)

where ψ is a function of space coordinates and g is a function of time t. For standing waves, there are several acceptable g functions and one of them is g(t) = e2πiνt ,

(1.4.2)

Introduction to Quantum Theory where frequency ν is related to propagation velocity v and wavelength λ by ν=

v . λ

(1.4.3)

If we substitute Φ(x, y, z, t) = ψ(x, y, z)e2πiνt

(1.4.4)

into eq. (1.3.2), we get e2πiνt ∇ 2 ψ =

1 ∂ 2 e2πiνt ψ v2 ∂t 2

= −4π 2 ν 2 v −2 e2πivt ψ,

(1.4.5)

or, upon canceling e2πivt , ∇ 2 ψ = −4π 2 ν 2 v −2 ψ.

(1.4.6)

Now we incorporate the corpuscular character (λ = h/p) into eq. (1.4.6) v = νλ = ν

# $ hν h = , p p

(1.4.7)

and eq. (1.4.6) becomes 2

∇ ψ=

#

−4π 2 p2 h2

$

ψ.

(1.4.8)

If we rewrite p2 in terms of kinetic energy T , or total energy E, and potential energy V , p2 = 2mT = 2m(E − V ),

(1.4.9)

the wave equation now has the form 2

∇ ψ=

#

−8mπ 2 h2

$

(E − V )ψ.

(1.4.10)

+ $ −h2 2 ∇ + V ψ = Eψ, 8π 2 m

(1.4.11)

Rearranging eq. (1.4.10) yields, *# or Hˆ ψ = Eψ,

(1.4.12)

11

12

Fundamentals of Bonding Theory where the Hamiltonian operator Hˆ is defined as Hˆ =

#

$ −h2 ∇2 + V . 8π 2 m

(1.4.13)

In other words, Hˆ has two parts: kinetic energy operator (−h2 /8π 2 m)∇ 2 and potential energy operator V . To summarize, the quantum mechanical way of studying the electronic structure of an atom or a molecule consists of the following steps: (1) Write down the Schrödinger equation of the system by filling in the proper potential energy. (2) Solve the differential equation to obtain the electronic energies Ei and wavefunctions ψi , i = 1, 2, . . . . (3) Use the wavefunctions ψi to determine the probability density functions |ψi |2 and the expectation values of physical observables. In the following, we use the ground state wavefunction ψ1s [eq. (1.3.6)] to determine the energy E1s of this state as well as the expectation values of the kinetic energy, , and potential energy, . By applying the Hamiltonian operator of the hydrogen atom on ψ1s , we can readily obtain E1s : Hˆ ψ1s =

*#

# 2 $+ $ −h2 e 2 ψ1s ∇ − 4π ε0 r 8π 2 m

= E1s ψ1s ,

(1.4.14)

$

(1.4.15)

and E1s =

#

1 4πε0

−e2 2a0

$#

= −2.18 × 10−18 J = −13.6 eV.

The expectation value of potential energy, , can also be computed easily: =

'

=

#

2π

0

dφ

−1 4πε0

'

π 0

$#

sin θdθ e2 a0

$

'

0

∞!

πa03

"−1

e

− ar

0

#

−e2 4π ε0 r

$

e

− ar

.

0

r 2 dr (1.4.16)

The quantity is simply the difference between E1s and : = E1s − =

#

1 4π ε0

$#

e2 2a0

$

.

(1.4.17)

Introduction to Quantum Theory Comparing eqs. (1.4.16) and (1.4.17), we get = −

. 2

(1.4.18)

which is called the virial theorem for atomic and molecular systems. In the following section, we treat several systems quantum mechanically to illustrate the method introduced here. 1.5

Simple applications of the Schrödinger equation

In the four examples given below, a particle (or electron) is allowed to move freely. The only difference is the shape of the “box,” in which the particle travels. As will be seen later, different shapes give rise to different boundary conditions, which in turn lead to different allowed energies (eigenvalues) and wavefunctions (eigenfunctions). 1.5.1

Particle in a one-dimensional box

In this system, the box has only one dimension, with length a. The potential energy is zero inside the box and infinity at the boundary and outside the box. In other words, the electron can move freely inside the box and it is impossible for it to get out of the box. Mathematically ) 0, 0 < x < a; V = (1.5.1) ∞, 0 ≥ x or x ≥ a. So the Schrödinger equation has the form $# 2 $ # d ψ −h2 = Eψ, 8π 2 m dx2

(1.5.2)

or d2 ψ = dx2

#

−8π 2 mE h2

$

ψ = −α 2 ψ,

(1.5.3)

with α2 =

8π 2 mE . h2

(1.5.4)

Solutions of eq. (1.5.3) are ψ = A sin αx + B cos αx,

(1.5.5)

where A and B are constants to be determined by the boundary conditions defined by eq. (1.5.1). At x = 0 or x = a, the potential barrier is infinitely high and the particle cannot be found at or around those points, i.e. ψ (0) = ψ (a) = 0.

(1.5.6)

13

14

Fundamentals of Bonding Theory With ψ(0) = 0, we get B = 0.

(1.5.7)

A sin α a = 0,

(1.5.8)

Also, ψ(a) = 0 yields

which means either A or sin α a vanishes. Since the former is not acceptable, we have sin α a = 0,

(1.5.9)

or αa = nπ,

n = 1, 2, 3, . . ..

(1.5.10)

So, the wavefunctions have the form ψn (x) = A sin

! nπx " a

,

n = 1, 2, 3, . . ..

(1.5.11)

The constant A can be determined by normalization: '

0

a

2

2

|ψn | dx = A

'

a 0

sin2

! nπ x " a

dx = 1,

(1.5.12)

which leads to the following form for the wavefunctions: ψn (x) =

# $1 ! nπx " 2 2 . sin a a

(1.5.13)

Note that ψ has the unit of length−1/2 and ψ 2 has the unit of length−1 . By combining eqs. (1.5.4) and (1.5.10), the energy of the system can also be determined: nπ α= = a

#

8π 2 mE h2

$ 12

(1.5.14)

or En =

n2 h2 , 8ma2

n = 1, 2, 3, . . . .

(1.5.15)

Figure 1.5.1 summarizes the results of this particle-in-a-box problem. From this figure, it is seen that when the electron is in the ground state (n = 1), it is most likely found at the center of the box. On the other hand, if the electron is in the first excited state (n = 2), it is most likely found around x = a/4 or x = 3a/4.

Introduction to Quantum Theory !

! "

"

!

! "

! " ! 0

n=4

E4 = 16h2/8ma2

3

E3 = 9h2/8ma2

2

E2 = 4h2/8ma2

1

E1 = h2/8ma2 0

a

Fig. 1.5.1.

Pictorial representations of En , ψn (left), and |ψn |2 (right) for the particle in a one-dimensional box problem.

a

In the following, we calculate the expectation values and , where px is the momentum of the particle (recall this is a one-dimensional system), for the ground state of this system. First, = 2m = 2mE # 2 $ h h2 = (2m) = 2. 2 8ma 4a

(1.5.16)

Next, for , we need to make use of the fact that the quantum mechanical operator pˆ x for px is (−ih/2π )(∂/∂x). So # $' a ! πx " # −ih $ # ∂ $ ! πx " 2 = sin sin dx = 0. a a 2π ∂x a 0

(1.5.17)

So the mean momentum is zero, as the electron is equally likely to travel to the left or to the right. On the other hand, is not zero, as the square of a momentum is always positive. From statistics, the uncertainty of momentum, 'px , may be expressed in terms of and : &1 % 2 'px = − 2 =

h . 2a

15

(1.5.18)

16

Fundamentals of Bonding Theory In the following, again for the ground state, we calculate the mean value of position x as well as that of x2 : # $' a ! πx " ! πx " 2 sin x sin dx <x> = a a a 0 a = . (1.5.19) 2 This result can be obtained by simply examining the function |ψ1 |2 shown in Fig. 1.5.1. Meanwhile, # $' a ! πx " ! πx " 2 x2 sin dx sin <x2> = a a a 0 # $ 1 2 1 =a . (1.5.20) − 3 2π 2 Now we are ready to determine the uncertainty in x: % &1 2 'x = <x2 >− <x>2 =a

*#

1 12

$

−

#

1 2π 2

$+ 1 2

.

(1.5.21)

The product 'x · 'px satisfies the Uncertainty Principle: 'x'px = a

*#

1 12

$

−

#

1 2π 2

$+ 1 # 2

h 2a

$

h = 1.14 4π #

$

>

h . 4π

(1.5.22)

There is a less mathematical way to show that the results of this onedimensional box problem do conform to the Uncertainty Principle. The ground state, or minimum, energy of this system is h2 /8ma2 , which has a positive value. On the other hand, when this system is treated classically, the minimum energy would be zero. The residual energy of the (quantum) ground state, or the energy above the classical minimum, is called the zero-point energy. The existence of this energy implies that the kinetic energy, and hence the momentum, of a bound particle cannot be zero. If we take the ground state energy to be px2 /2m, we get the minimum momentum of the particle to be ±h/2a. The uncertainty in momentum, 'px , may then be approximated to be h/a. If we take the uncertainty in position, 'x, to be the length of the box, a, then 'x'px is (approximately) h, which is in accord with the Uncertainty Principle. The results of the particle in a one-dimensional box problem can be used to describe the delocalized π electrons in (linear) conjugated polyenes. Such an approximation is called the free-electron model. Take the butadiene molecule CH2 =CH–CH=CH2 as an example. The four π electrons of this system would fill up the ψ1 and ψ2 orbitals, giving rise to the (ψ1 )2 (ψ2 )2 configuration. If we excite one electron from the ψ2 orbital to the ψ3 orbital, we need an energy of 'E =

5h2 hc = . 2 λ 8ma

(1.5.23)

Introduction to Quantum Theory The length of the box, a, may be approximated in the following way. Typical C–C and C=C bond lengths are 154 and 135 pm, respectively. If we allow the π electrons to move a bit beyond the terminal carbon atoms, the length of the box may be rounded off to (4 × 1.40 =) 560 pm. If a is taken to be this value, λ in eq. (1.5.23) can be calculated to be 207.0 nm. Experimentally, butadiene absorbs light at λ = 210.0 nm. So, even though the model is very crude, the result is fortuitously good. The free-electron model breaks down readily when it is applied to longer polyenes. For hexatriene, we have a = 6 × 1.40 = 840 pm, 'E = E4 − E3 , and λ = 333 nm. Experimentally this triene absorbs at λ = 250 nm. For octatetraene, the box length a now becomes 1120 pm, and 'E = E5 − E4 with λ = 460 nm, compared to the experimental value of 330 pm. Despite this shortcoming, the model does predict that when a conjugated polyene is lengthened, its absorption band wavelength becomes longer as well. When a polyene reaches a certain length, its absorption wavelength will appear in the visible region, i.e. λ is between 400 and 700 nm. When this occurs, the polyene is colored. One of the better known colored polyenes is β-carotene, which is responsible for orange color of carrots. It has the structure:

This polyene has 11 conjugated π bonds, with λ = 450 nm. Carotene can be cleaved enzymatically into two units of all-trans-vitamin A, which is a polyene with five conjugated π bonds:

CH2OH

The absorption peak of this compound appears at λ = 325 nm. This molecule plays an important role in the chemistry of vision. 1.5.2

Particle in a three-dimensional box

The potential energy of this system has the form V =

)

0, 0 < x < a ∞, 0 ≥ x ≥ a

and or

0 < y < b and 0 ≥ y ≥ b or

0 < z < c, 0 ≥ z ≥ c.

(1.5.24)

17

18

Fundamentals of Bonding Theory So the Schrödinger equation now is #

$ −h2 ∇ 2 ψ = Eψ. 8π 2 m

(1.5.25)

To solve this equation, we make use of the technique of separation of variables ψ(x, y, z) = X (x)Y (y)Z(z),

(1.5.26)

where X , Y , and Z are one-variable functions involving variables, x, y, and z, respectively. Substituting eq. (1.5.26) into eq. (1.5.25) leads to ∇ 2ψ =

*#

∂2 ∂x2

$

+

#

#

∂ 2Y ∂y2

∂2 ∂y2

$

+

#

∂2 ∂z 2

#

∂ 2Z ∂z 2

$+

XYZ =

#

−8π 2 mE h2

$

XYZ, (1.5.27)

or YZ

#

∂ 2X ∂x2

$

+ XZ

$

+ XY

$

=

#

−8π 2 mE h2

$

XYZ.

(1.5.28)

Dividing eq. (1.5.28) by XYZ yields. 1 X

#

∂ 2X ∂x2

$

+

1 Y

#

∂ 2Y ∂y2

$

+

1 Z

#

∂ 2Z ∂z 2

$

=

−8π 2 mE . h2

(1.5.29)

Now it is obvious that each of the three terms on the left side of eq. (1.5.29) is equal to a constant: 1 X 1 Y 1 Z

#

∂ 2X ∂x2

# #

∂ 2Y ∂y2 ∂ 2Z ∂z 2

$

= −αx2 ,

(1.5.30)

$

= −αy2 ,

(1.5.31)

$

= −αz2 ,

(1.5.32)

with the constraint on the constants being αx2 + αy2 + αz2 =

8π 2 mE . h2

(1.5.33)

In other words, each degree of freedom makes its own contribution to the total energy: αx2 =

8π 2 mEy 8π 2 mEx 8π 2 mEz 2 2 , α = , α = , y z h2 h2 h2

(1.5.34)

Introduction to Quantum Theory and E = Ex + Ey + Ez .

(1.5.35)

Each of eqs. (1.5.30) to (1.5.32) is similar to that of the one-dimensional problem, eq. (1.5.2) or (1.5.3). Hence the solutions of eqs. (1.5.30) to (1.5.32) can be readily written $ # $1 # 2 2 jπx Xj (x) = , j = 1, 2, 3, . . . , sin a a $ # $1 # 2 2 kπy , k = 1, 2, 3, . . . , sin Yk (y) = b b $ # $1 # 2 2 2π z , 2 = 1, 2, 3, . . . . sin Z2 (z) = c c

(1.5.36) (1.5.37) (1.5.38)

The total wavefunction, as given by eq. (1.5.26), then becomes 8 ψj,k,2 (x, y, z) = abc #

$1 2

$ # $ # $ kπy 2πz jπx sin sin , sin a b c #

j, k, 2 = 1, 2, 3, . . . .

(1.5.39)

Now ψ has the unit of volume−1/2 and |ψ|2 has the unit of volume−1 , as expected for a probability density function of a three-dimensional system. As in the case of the wavefunctions, the energy of the system is also dependent on three quantum numbers: Ej,k,2 = (Ex )j + (Ey )k + (Ez )2 # 2 $ *# 2 $ # 2 $ # 2 $+ h k 2 j = + + 2 , 8m a2 b2 c

j, k, 2 = 1, 2, 3, . . . . (1.5.40)

When the box is a cube, i.e. a = b = c, eq. (1.5.40) becomes # 2 $ h Ej,k,2 = (j2 + k 2 + 22 ), j, k, 2 = 1, 2, 3, . . . . 8ma2

(1.5.41)

An interesting feature of the energy expression given by eq. (1.5.41) is that different states, with different sets of quantum numbers and different wavefunctions, can have the same energy. When different states have the same energy, they are called degenerate states. For examples, E1,1,2 = E1,2,1 = E2,1,1 =

3h2 , 4ma2

(1.5.42)

or E1,2,3 = E2,1,3 = E1,3,2 = E3,1,2 = E3,2,1 = E2,3,1 =

7h2 . 4ma2

(1.5.43)

19

20

Fundamentals of Bonding Theory Now we will apply the particle in a three-dimensional box model to a chemical problem. When sodium vapor is passed over a crystal of NaCl, the crystal exhibits a greenish-yellow color, which is the result of the process δNa(g) + NaCl(c) −→ (Na+ )1+δ (Cl− eδ− )(c), Na+

e–

Fig. 1.5.2.

A color center (marked e− ) in a sodium halide crystal. Note that the electronic position is an anionic site. Also, for simplicity, anions are not shown here.

δ > r1, Zeff for e2 is ~1

r2 –e2 +2e

electron 1

r2 1 and 1 − Sab < 1 and this leads to the result that the bonding effect is smaller than the antibonding effect. If we ignore the overlap of the atomic orbitals by setting Sab = 0, the bonding effect would be the same as the antibonding effect. ∗ as well Now we examine the bonding orbital σ1s and antibonding orbital σ1s ∗ 2 2 as their probability density functions |σ1s | and |σ1s | . A schematic representation of σ1s is shown in Fig. 3.1.5(a). In this combination of two 1s orbitals, electron density accumulates in the internuclear region. Also, σ1s has cylindrical symmetry around the internuclear axis.

H

H2+

H+ σ1s* ! ψA

1sa

E

1sb σ1s ! ψS

Fig. 3.1.4.

A simplified energy level diagram for H+ 2.

Nodal plane – +

+

z

z Fig. 3.1.5.

(a)

(b)

Molecular orbitals of H+ 2 : (a) σ1s , ∗. (b) σ1s

84

Fundamentals of Bonding Theory Nodal plane

Fig. 3.1.6.

Probability density distribution of H+ 2 plotted along the internuclear axis: ∗ 2 2 (a) |σ 1s | , (b) |σ 1s | .

(a)

(b)

∗ is shown. It is seen that this In Fig. 3.1.5(b), a schematic drawing for σ1s combination of 1s orbitals has no charge accumulation between the nuclei. Indeed, in the nodal plane there is zero probability of finding an electron. As ∗ orbital also has cylindrical symmetry around the in the case of σ1s , the σ1s molecular axis. The accumulation of charge density between the nuclei in σ1s is clearly seen when we consider the probability density function |σ1s |2 :

|σ1s |2 = |1sa + 1sb |2

= |1sa |2 + 2|1sa ||1sb | + |1sb |2 .

(3.1.37)

When we plot this function along the internuclear axis, Fig. 3.1.6(a) is obtained. In this figure, the build-up of charge density between the nuclei is obvious. ∗ , we have the probability density function For the antibonding orbital σ1s ∗ 2 | = |1sa − 1sb |2 |σ1s

= |1sa |2 − 2|1sa ||1sb | + |1sb |2 .

(3.1.38)

∗ |2 along the internuclear axis, we get Fig. 3.1.6(b). Now there is If we plot |σ1s a clear deficiency of charge density between the nuclei.

3.1.4

Essentials of molecular orbital theory

In sections 3.1.2 and 3.1.3, we use the example of H+ 2 to illustrate the molecular orbital theory. In particular, we note the following: (1) Since molecular orbitals are linear combinations of atomic orbitals, it follows that n atomic orbitals will generate n molecular orbitals. (2) If we have n atomic orbitals forming n molecular orbitals, “usually” half of the molecular orbitals are bonding, while the other half are antibonding. However, this condition does not always hold. For instance, if we have three atomic orbitals to form three molecular orbitals, obviously half of the latter cannot be bonding. Also, there is an additional type that we have not yet considered: nonbonding molecular orbitals, which by definition neither gains nor loses stability (or energy). (3) Bonding molecular orbitals have two characteristics: its energy is lower than those of the constituent atomic orbitals and there is a concentration of charge density between the nuclei.

Covalent Bonding in Molecules + + Table 3.1.1. Molecular orbital theory applied to H2 , H2 , He2 , and He2

Molecule Configuration Bond energy Bond length Remark (kJ mol−1 ) (pm) H+ 2

1 σ1s

255

106

H2

2 σ1s

431

74

He+ 2

2 σ ∗1 σ1s 1s

251

108

He2

2 σ ∗2 σ1s 1s

Repulsive state

The bond is formed by one bonding electron. There are now two bonding electrons. Hence the bond is stronger and shorter than that in H+ 2. This bond is slightly weaker than that in H+ 2 , since antibonding effect is greater than bonding effect. The gain of energy by the bonding electrons is more than offset by the antibonding electrons. Hence there is no bond in He2 .

(4) On the other hand, the energy of an antibonding molecular orbital is higher than those of the constituent atomic orbitals. Also, the wavefunction of an antibonding orbital has one or more nodes between the nuclei. Hence there is a deficiency of charge density between the nuclei. To conclude this section, we apply the energy level diagram in Fig. 3.1.4 to four simple molecules having one to four electrons. The results are summarized in Table 3.1.1. Examining Table 3.1.1, we see that our simple treatment is able to rationalize, at least semi-quantitatively, the formation of H2 and the non-existence of He2 . 3.2 3.2.1

The hydrogen molecule: molecular orbital and valence bond treatments Molecular orbital theory for H2

In our previous discussions on H+ 2 , we saw that the lone electron occupies the σ1s molecular orbital: σ1s = (2 + 2Sab )−1/2 (1sa + 1sb ).

(3.2.1)

The molecular orbital theory was first introduced by F. Hund (of the Hund’s rule fame) and R. S. Mullikan, with the latter winning the Nobel Prize in chemistry in 1966. Since σ1s can accommodate two electrons, in molecular orbital theory, the wavefunction for H2 is ψ(1, 2) = σ1s (1)σ1s (2)

= (2 + 2Sab )−1/2 [1sa (1) + 1sb (1)]

× (2 + 2Sab )−1/2 [1sa (2) + 1sb (2)].

(3.2.2)

From this function, we can see that both electrons in H2 reside in the ellipsoidal σ1s orbital. This situation is similar to that of the helium atom, where both

85

86

Fundamentals of Bonding Theory electrons reside in the spherical 1s orbital, with wavefunction 1s(1)1s(2). It is important to appreciate that, in σ1s , the identity of the atomic orbital is lost. This is the essential tenet of molecular orbital theory. When we use eq. (3.2.2) to determine the energy of H2 , we obtain De = 260 kJ mol−1 and re = 85 pm, while the experimental results are 458 kJ mol−1 and 74 pm, respectively. If we vary the nuclear charge, we obtain Zeff = 1.197, De = 337 kJ mol−1 , and re = 73 pm. So while the quantitative results may only be called fair, we do get a stable H2 molecule. 3.2.2

Valence bond treatment of H2

Historically, molecular orbital theory was preceded by an alternative and successful description of the bonding in H2 . In 1927, W. Heitler and F. London proposed the valence bond theory, in which each electron resides in an atomic orbital. In other words, in this model, the identity of the atomic orbital is preserved. There are two ways in which the two electrons in H2 can be accommodated in the pair of 1s atomic orbitals: (a) Electron 1 in a 1s orbital centered at nucleus a and electron 2 in a 1s orbital centered at nucleus b. Mathematically: ψI (1, 2) = 1sa (1)1sb (2).

(3.2.3)

(b) Electron 1 in orbital 1sb and electron 2 in 1sa , or, ψII (1, 2) = 1sb (1)1sa (2).

(3.2.4)

The valence bond wavefunction for H2 is simply a linear combination of ψI and ψII : ψ(1, 2) = cI ψI + cII ψII

= cI 1sa (1)1sb (2) + cII 1sb (1)1sa (2),

(3.2.5)

where the coefficients cI and cII are to be determined by the variational method. To do that, we once again need to solve a secular determinant: , , ,HI I − ESI I HI II − ESI II ,, , (3.2.6) ,HI II − ESI II HII II − ESII II , = 0,

Upon solving for E, we substitute E into the following secular equations to obtain coefficient cI and cII : ) (HI I − ESI I )cI + (HI II − ESI II )cII = 0 . (3.2.7) (HI II − ESI II )cI + (HII II − ESII II )cII = 0

With HI I = HII II and SI I = SII II , the roots of eq. (3.2.6) are E+ = (HI I + HI II )/(1 + SI II ), E− = (HI I − HI II )/(1 − SI II ).

(3.2.8) (3.2.9)

Covalent Bonding in Molecules

87 e1

A diagram illustrating the various distances in H2 is shown in Fig. 3.2.1. The Hamiltonian operator for this system, in a.u., is

r12

e2

ra1

1 1 1 1 1 1 1 1 Hˆ = − ∇12 − ∇22 − − − − + + . 2 2 ra1 rb1 ra2 rb2 r12 rab

ra2

(3.2.10) a

In the following, we evaluate the various Hij and Sij integrals: 1sa (1)1sb (2) · 1sa (1)1sb (2)dτ1 dτ2 SI I = SII II = ' ' = |1sa (1)|2 dτ1 · |1sb (2)|2 dτ2 = 1.

Fig. 3.2.1.

(3.2.11)

''

1sa (1)1sb (2) · 1sb (1)1sa (2)dτ1 dτ2 ' ' = 1sa (1)1sb (1)dτ1 · 1sa (2)1sb (2)dτ2 2 = Sab ,

(3.2.12)

where Sab is simply the overlap integral introduced in the treatment of H+ 2. Meanwhile, HI I = HII II =

''

1sa (1)1sb (2)Hˆ 1sa (1)1sb (2)dτ1 dτ2

1 + J1 − 2J2 , rab

= 2E1s +

(3.2.13)

where J1 and J2 are called Coulomb integrals: 1 |1sa (1)1sb (2)|2 dτ1 dτ2 , r12 '' 1 |1sa (1)1sb (2)|2 dτ1 dτ2 J2 = ra2 '' 1 |1sa (1)1sb (2)|2 dτ1 dτ2 . = rb1 J1 =

''

(3.2.14)

(3.2.15)

Finally, HI II =

''

rab

The molecular system of H2 .

''

SI II =

rb1

1sa (1)1sb (2)Hˆ 1sb (1)1sa (2)dτ1 dτ2

2 = 2E1s Sab +

2 Sab + K1 − 2K2 , rab

(3.2.16)

rb2

b

88

Fundamentals of Bonding Theory where K1 and K2 are called resonance integrals: '' 1 |1sa (1)1sb (2)1sb (1)1sa (2)| dτ1 dτ2 , K1 = r12 '' 1 |1sa (1)1sb (2)1sb (1)1sa (2)| dτ1 dτ2 K2 = ra1 '' 1 |1sa (1)1sb (2)1sb (1)1sa (2)| dτ1 dτ2 . = rb1

(3.2.17)

(3.2.18)

Substituting Hij and Sij into eqs. (3.2.8) and (3.2.9), we obtain E+ = 2E1s + E− = 2E1s +

1 J1 − 2J2 + K1 − 2K2 + 2 rab 1 + Sab 1 J1 − 2J2 − K1 + 2K2 + 2 rab 1 − Sab

(3.2.19) (3.2.20)

Note the integrals J1 , J2 , K1 , and K2 are all functions of rab . When we plot E+ and E− against rab , we get the energy curves shown in Fig. 3.2.2. So, once again, the valence bond treatment yields a stable H2 molecule, even though the quantitative results do not match exactly the experimental data. Upon substituting E+ into eq. (3.2.7), we get cI = cII . After normalization, the wavefunction becomes 2 −1/2 ) [1sa (1)1sb (2) + 1sb (1)1sa (2)]. ψ+ = (2 + 2Sab

(3.2.21)

Also, with E− , we get cI = −cII . After normalization, the wavefunction becomes: 2 −1/2 ) [1sa (1)1sb (2) − 1sb (1)1sa (2)]. ψ− = (2 − 2Sab

(3.2.22)

After a simple valence bond treatment of H2 , we now proceed to study the excited states of H2 . Through this discussion, we will recognize that the molecular orbital and valence bond treatments, after modification, can bring about the same quantitative results.

E E– rab E = 2E1s Fig. 3.2.2.

Valence bond energies E+ and E− plotted as functions of rab .

E+ Eexp

Covalent Bonding in Molecules 3.2.3

Equivalence of the molecular orbital and valence bond models

As discussed previously, the bonding molecular orbital of H2 is σ1s = (2 + 2Sab )−1/2 (1sa + 1sb ),

(3.2.23)

and the antibonding molecular orbital has the form ∗ = (2 − 2Sab )−1/2 (1sa − 1sb ). σ1s

(3.2.24)

2 , with the (unnormalized) wavefunction The ground configuration of H2 is σ1s 2 ) = [1sa (1) + 1sb (1)] × [1sa (2) + 1sb (2)]. ψ1 (σ1s

(3.2.25)

Upon adding the spin part, the total wavefunction for the ground state of H2 is 2 ) = [1sa (1) + 1sb (1)][1sa (2) + 1sb (2)][α(1)β(2) − β(1)α(2)] ψ1 (σ1s , , ,σ α(1) σ1s β(1), ,. = ,, 1s (3.2.26) σ1s α(2) σ1s β(2),

Clearly, this is a spin singlet state. ∗2 has the wavefunction Similarly, the excited configuration σ1s

∗2 ) = [1sa (1) − 1sb (1)][1sa (2) − 1sb (2)][α(1)β(2) − β(1)α(2)] ψ2 (σ1s , , ∗ ,σ α(1) σ ∗ β(1), 1s , (3.2.27) = ,, 1s ∗ α(2) σ ∗ β(2), . σ1s 1s

This is also a spin singlet state. Furthermore, this is a repulsive state; i.e., it is not a bound state. 1 σ ∗1 , there are two states, one singlet and one For the excited configuration σ1s 1s triplet. This situation is similar to that found in the excited configuration 1s1 2s1 of the helium atom. The singlet and triplet wavefunctions for these excited configurations are: 1 ∗1 ∗ ∗ σ1s ; S = 0) = [σ1s (1)σ1s (2) + σ1s (2)σ1s (1)][α(1)β(2) − β(1)α(2)] ψ3 (σ1s

(3.2.28)  [α(1)β(2) + β(1)α(2)] 1 ∗1 ∗ ∗ α(1)α(2). ψ4 (σ1s σ1s ; S = 1) = [σ1s (1)σ1s (2) − σ1s (2)σ1s (1)]  β(1)β(2) (3.2.29) On the other hand, the (un-normalized) ground (ψ+ ) and excited (ψ− ) state valence bond wavefunctions are ψ+ = 1sa (1)1sb (2) + 1sb (1)1sa (2)

ψ− = 1sa (1)1sb (2) − 1sb (1)1sa (2).

(3.2.30) (3.2.31)

89

90

Fundamentals of Bonding Theory Expanding the wavefunction in eq. (3.2.25), we get 2 ψ1 (σ1s ) = [1sa (1)1sb (2) + 1sb (1)1sa (2)] + [1sa (1)1sa (2) + 1sb (1)1sb (2)]

= ψ+ + ψi ,

(3.2.32)

where ψi = 1sa (1)1sa (2) + 1sb (1)1sb (2).

(3.2.33)

Wavefunction ψi refers to the situation where both electrons are on nucleus a or nucleus b, i.e., ionic structures. Now it is obvious that the valence bond wavefunction ψ+ considers only covalent structure, while the molecular orbital wavefunction ψ1 has an equal mixture of covalent and ionic contributions. Similarly, expanding the wavefunction in eq. (3.2.27) yields ∗2 ψ2 (σ1s ) = −[1sa (1)1sb (2) + 1sb (1)1sa (2)] + [1sa (1)1sa (2) + 1sb (1)1sb (2)]

= −ψ+ + ψi .

(3.2.34)

∗2 is also an equal mixture So the wavefunction for the excited configuration σ1s of covalent and ionic parts, except now that the linear combination coefficients have different signs. Solving eqs. (3.2.32) and (3.2.34) for ψ + , we get

ψ+ = ψ1 − ψ2 .

(3.2.35)

So, put another way, the valence bond wavefunctions for the ground state of H2 2 and σ ∗2 , and the combination has equal contributions from configurations σ1s 1s coefficients have different signs. Such a wavefunction, which employs a mixture of configurations to describe the electronic state of an atom or molecule, is called a configuration interaction (CI) wavefunction. It is obvious that the deficiency of ψ+ is that it does not take ionic contributions (ψi ) into account. Conversely, ψ1 suffers from too much (50%) contribution from the ionic structures. To get the wavefunction with optimal ionic contribution, we set , ψ+ = c+ ψ+ + ci ψi ,

(3.2.36)

where coefficient c+ and ci are to be determined through the following 2×2 secular determinant and the associated secular equations: , , , H++ − ES++ H+i − ES+i , , ,=0 (3.2.37) , H+i − ES+i Hii − ESii , ) (H++ − ES++ )c+ + (H+i − ES+i )ci = 0 . (3.2.38) (H+i − ES+i )c+ + (Hii − ESii )ci = 0 The result of this optimization process is ci /c+ = 0.16. In other words, the optimal wavefunction has ionic and covalent contributions in the ratio of about 1:6. Such a dominance of covalent character is expected for a molecule such as H2 .

Covalent Bonding in Molecules Table 3.2.1. Optimized dissociation energies and equilibrium bond lengths from trial wavefunctions for H2 with adjustable parameters

De (kJ mol−1 ) re (pm)

Trial wavefunction [1sa (1) + 1sb (1)] [1sa (2) + 1sb (2)], eq. (3.2.1); Z = 1 [1sa (1) + 1sb (1)] [1sa (2) + 1sb (2)], eq. (3.2.1); Zeff = 1.197 1sa (1)1sb (2) + 1sb (1)1sa (2), eq. (3.2.30); Z = 1 1sa (1)1sb (2) + 1sb (1)1sa (2), eq. (3.2.30); Zeff = 1.166 c[1sa (1)1sb (2) + 1sb (1)1sa (2)] + [1sa (1)1sa (2) + 1sb (1)1sb (2)], eqs. (3.2.30), (3.2.33), and (3.2.36); Z = 1 and c = 6.322 c[1sa (1)1sb (2) + 1sb (1)1sa (2)] + [1sa (1)1sa (2) + 1sb (1)1sb (2)], eqs. (3.2.30), (3.2.33), and (3.2.36); Zeff = 1.194 and c = 3.78 φa (1)φb (2) + φb (1)φa (2), φ = 1s + λ2pz (a “polarized” atomic function); Zeff (1s) = Zeff (2p) = 1.190, λ = 0.105 c[φa (1)φb (2) + φb (1)φa (2)] + [1sa (1)1sa (2) + 1sb (1)1sb (2)], φ = 1s + λ2pz ; Zeff (1s) = Zeff (2p) = 1.190, c = 5.7, λ = 0.07 Four-parameter function by Hirschfelder and Linnett (1950) Thirteen-term function by James and Coolidge (1933) One hundred-term function by Kołos and Wolniewicz (1968) Experimental

260.0 336.5 304.5 364.9 311.6

85.2 73.0 86.8 74.6 88.4

388.4

75.6

389.8

74.9

397.7

74.6

410.1 455.7 458.1 458.1

76.2 74.1 74.1 74.1

Similarly, we can also improve ψ1 by mixing in an optimal amount of ψ2 : ψ1, = c1 ψ1 + c2 ψ2 .

(3.2.39)

The optimal c2 /c1 ratio is −0.73. More importantly, the improved valence bond , and the improved molecular orbital wavefunction ψ , are wavefunction ψ+ 1 one and the same, thus showing these two approaches can lead to identical quantitative results. Table 3.2.1 summarizes the results of various approximate wavefunctions for the hydrogen molecule. This list is by no means complete, but it does show that, as the level of sophistication of the trial function increases, the calculated dissociation energy and bond distance approach closer to the experimental values. In 1968, W. Kołos and L. Wolniewicz used a 100-term function to obtain results essentially identical to the experimental data. So the variational treatment of the hydrogen molecule is now a closed topic. 3.3

Diatomic molecules

After the treatments of H+ 2 and H2 , we are ready to take on other diatomic molecules. Before we do that, we first state two criteria governing the formation of molecular orbitals: (1) For two atomic orbitals φa and φb to form a bonding and antibonding molecular orbitals, φa and φb must have a non-zero overlap, i.e., ' Sab = φa φb dτ ' = 0. (3.3.1) Furthermore, for Sab ' = 0, φa and φb must have the same symmetry. In Fig. 3.3.1, we can see that there is net overlap in the left and middle cases,

91

92

Fundamentals of Bonding Theory

Fig. 3.3.1.

Non-zero overlap in the two cases shown on the left and in the middle, and zero overlap in the case shown on the right.

A

B

A

B

A

B

while Sab vanishes in the case shown on right. The concept of symmetry will be studied more fully in Chapters 6 and 7, when the topic of group theory is taken up. (2) The second criterion is the energy factor: for φa and φb to have significant bonding (and antibonding) effect, they should have similar energies. This is why, in our treatments of H2 and H+ 2 , we are only concerned with the interaction between two 1s orbitals. We ignore the interaction between, say, the 1s orbital on Ha and the 2s orbital on Hb . These two atomic orbitals do have non-zero overlap between them. But these orbitals do not bond (or interact) effectively because they have very different energies. 3.3.1

Homonuclear diatomic molecules

Now we proceed to discuss homonuclear diatomics with 2s and 2p valence orbitals. Starting from these atomic orbitals, we will make (additive and subtractive) combinations of them to form molecular orbitals. In addition, we also need to know the energy ordering of these molecular orbitals. We first consider the 2s orbitals.As in the cases of H+ 2 and H2 , the combination of (2sa +2sb ) leads to a concentration of charge between the nuclei. Hence it is a σ bonding orbital and is called σs . On the other hand, the (2sa −2sb ) combination has a nodal plane between the nuclei and there is a charge deficiency in this region. Hence this is a σ antibonding orbital, which is designated as σs∗ . For the 2p orbitals, there are two types of overlap. We first note that the two pz orbitals both lie along the internuclear axis (conventionally designated as the z axis), while the px and py orbitals are perpendicular to this axis. Once again, 2pza + 2pzb leads to a bonding orbital called σz , while the combination 2pza − 2pzb is an antibonding molecular orbital called σz∗ . It is seen that these two molecular orbitals also have cylindrical symmetry around the internuclear axis. So both of them are σ orbitals. The overlap between the 2pxa and 2pxb orbitals occurs in two regions, which have the same size and shape but carry opposite signs: one above the yz plane and the other below it. As there is no longer cylindrical symmetry around the nuclear axis, the molecular orbital is not a σ type. Rather, it is called a πx orbital, which is characterized by a change in sign across the yz plane (a nodal plane). In an analogous manner, the combination 2pxa − 2pxb leads to the antibonding πx∗ orbital, which is composed of four lobes of alternating signs partitioned by two nodal planes. Similarly, there are the corresponding bonding πy (2pya + 2pyb ) and antibonding πy∗ (2pya − 2pyb ) molecular orbitals.

Covalent Bonding in Molecules

93

Before we proceed to discuss the energy order of these molecular orbitals, it is important to note that the 2px orbital on atom a has zero overlap with either 2py or 2pz on atom b; in other words, the pair of orbitals do not have compatible symmetry. Therefore, among the six 2p orbitals on the two atoms, 2pxa interacts only with 2pxb , 2pya with 2pyb , and 2pza with 2pzb . Furthermore, the πx and πy orbitals have the same energy; i.e., they are doubly degenerate. Similarly, the πx∗ and πy∗ orbitals compose another degenerate set at a higher energy. To summarize briefly at this point: referring to Fig. 3.3.2, we have started with eight atomic orbitals (one 2s and three 2p orbitals on each atom) and ∗ , σ , σ ∗, π , π ∗, π , have constructed eight molecular orbitals, σ2s , σ2s z x y z x ∗ and πy . The relative energies of these molecular orbitals can be determined from experiments such as spectroscopic measurements or from calculations. For homonuclear diatomics, there are two energy level schemes, as shown in Fig. 3.3.2. In each scheme, the eight molecular orbitals form six energy levels and can accommodate up to 16 electrons. The scheme on the right is applicable to atoms whose 2s–2p energy difference is small, while the scheme on the left is for atoms with a large 2s–2p energy gap. (Recall, from Fig. 3.3.1, s orbitals can overlap with p orbitals to form σ molecular orbitals. Whether this interaction is important depends on the energy difference between the interacting atomic orbitals.) The experimental 2s–2p energy differences of the elements of the second period are summarized in Table 3.3.1. It can be readily seen that O and F have the largest 2s–2p gap. Hence the energy ordering shown on the left side of Fig. 3.3.2 is applicable to O2 and F2 . On the other hand, the energy scheme on the right side of Fig. 3.3.2 is applicable for Li2 , Be2 , B2 , C2 , and N2 . Furthermore, the only difference between the two scheme is the relative ordering of the σz and 2σu + – + –

+ –

+ –

– +

+ –

x

y

+

–

∗ ∗ π2p π2p y x

1πg

2σg π2py π2p

1πu

+ –

+ – + –

– +

– + + –

∗ σ2s

Fig. 3.3.2.

1σu +

– +

σ2pz

z +

+

∗ π2p z

x

– + + –

–

+ –

+ +

– +

+ –

σ2s 1σg

The shapes and energy ordering of the molecular orbitals for homonuclear diatomic molecules. The scheme on the left is applicable to O2 and F2 , while that on the right is applicable to other diatomics of the same period.

94

Fundamentals of Bonding Theory Table 3.3.1. The 2s–2p energy gap of the second-row elements

Element −E2s (eV) −E2p (eV) E2p − E2s (eV)

Li

Be

B

C

N

O

5.39 3.54 1.85

9.32 6.59 2.73

12.9 8.3 4.6

16.6 11.3 5.3

20.3 14.5 5.8

28.5 13.6 14.9

F 37.8 17.4 20.4

degenerate (πx , πy ) levels. For O2 and F2 , there is no significant s–p mixing, due to the larger 2s–2p energy gaps of O and F. On the other hand, for the remaining homonuclear diatomics of the same period, through s–p mixing, the molecular orbitals are no longer called σs , σs∗ , σz , σz∗ , etc. Instead they are now called σg , σu , etc., where g indicates centrosymmetry and u indicates antisymmetry with respect to the molecular center. Table 3.3.2. Electronic configurations and structural parameters of homonuclear diatomic molecules of the second period

X2

Electronic configuration

Bond length (pm)

Li2 Be2 B2 C2 C2− 2 N2 N+ 2 N2− 2 O2 O+ 2 O− 2 O2− 2 F2

1σg2 1σg2 1σu2 1σg2 1σu2 1πu2 1σg2 1σu2 1πu4 1σg2 1σu2 1πu4 2σg2 1σg2 1σu2 1πu4 2σg2 1σg2 1σu2 1πu4 2σg1 σs2 σs∗2 σz2 πx2 πy2 πx∗1 πy∗1 σs2 σs∗2 σz2 πx2 πy2 πx∗1 πy∗1 σs2 σs∗2 σz2 πx2 πy2 πx∗1 σs2 σs∗2 σz2 πx2 πy2 πx∗2 πy∗1 σs2 σs∗2 σz2 πx2 πy2 πx∗2 πy∗2 σs2 σs∗2 σz2 πx2 πy2 πx∗2 πy∗2

267.2 — 158.9 124.25 120 109.76 111.6 122.4 120.74 112.27 126 149 141.7

Bonding energy (kJ mol−1 ) 110.0 — 274.1 602 — 941.69 842.15 — 493.54 626 392.9 138 155

Bond order

1 0 1 2 3 3 21/2 2 2 21/2 11/2 1 1

Table 3.3.2 summarizes the various properties of second-row homonuclear diatomic molecules. In the last column of the table, we list the “bond order” between atoms A and B in the molecule AB. Simply put, the bond order is a number that gives an indication of its strength relative to that of a two-electron 1 2 single bond. Thus the bond order of H+ 2 (σ1s ) is 1/2, while that of H2 (σ1s ) is 1. For a system with antibonding electrons, we take the simplistic view that one antibonding electron “cancels out” one bonding electron. Thus the bond orders 2 ∗1 2 ∗2 in He+ 2 (σ1s σ1s ) and He2 (σ1s σ1s ) are 1/2 and 0, respectively, and helium is not expected to form a diatomic molecule. Some interesting points are noted from the results given in Table 3.3.2: (1) The bond in Li2 is longer and weaker than that in H2 (74 pm; 431 kJ mol−1 ). This is because the bond in Li2 is formed by 2s valence electrons that lie outside filled 1s atomic orbitals.

Covalent Bonding in Molecules

95

(2) The diatomic molecule Be2 is unstable; the ground state is a repulsive state. As in He2 , the stabilization gained by the bonding electrons is more than offset by the destabilizing antibonding electrons. (3) The bond in B2 is stronger than that in Li2 because B has a smaller atomic radius than Li. Also, B2 has two unpaired electrons in the 1πu orbital and is hence a paramagnetic species. (4) The bond length and bond energy in C2 are compatible with the double bond predicted by molecular orbital theory. It is noted that the 2σg orbital is only slightly higher in energy than 1πu . Indeed, C2 absorbs light in the visible region at 19,300 cm−1 . This corresponds to exciting an electron from the 1πu molecular orbital to the 2σg orbital. This is a fairly small excitation energy for a diatomic molecule, since electronic excitations for other diatomics are usually observed in the ultraviolet region. (5) The bond in N2 is a triple bond, in agreement with the Lewis structure :N≡N: of this molecule. We now can see that the lone pairs in the Lewis structure correspond to the 1σg2 and 1σu2 electrons; the two pairs of bonding and antibonding electrons result in no net bonding. The three bonds in the Lewis structure correspond to the 1πu4 and 2σg2 electrons in molecular orbital theory. The electronic excitation from the 2σg orbital to 1πg orbital occurs at around 70,000 cm−1 in the vacuum ultraviolet region. The experimental energy ordering of the molecular orbitals for the N2 molecule is shown in Fig. 3.3.3(a). Upon losing one electron to form N+ 2 , there is not much change in bond length, as the electron is from a weakly bonding 2σg orbital. In a recently determined crystal structure of SrN2 , the bond length found for the diazenide anion (N2− 2 ) is compatible with the theoretical bond order of 2. (6) Molecular orbital theory predicts that O2 is paramagnetic, in agreement with experiment. Note that the Lewis structure of O2 does not indicate that it has two unpaired electrons, even through it does imply the presence of a double bond. In fact, the prediction/confirmation of paramagnetism in O2 was one of the early successes of molecular orbital theory. Also, the ions O+ 2 2− (dioxygen cation), O− 2 (superoxide anion), and O2 (peroxide anion) have bond orders 21/2, 11/2, and 1, respectively. The experimental energy levels of the molecular orbital for the O2 molecule are shown in Fig. 3.3.3(b). (7) Fluorine F2 , is isoelectronic with O2− 2 . Hence they have similar bond lengths as well as similar bond energies. Finally, molecular orbital theory

–7.0 –15.6 –17.0 –18.8

1πg (LUMO) 2σg(HOMO) 1πu 1σu

1σg

–37.0

N2

(b) ∗ π2p

–12.5 E (eV)

E (eV)

(a)

σ2p

–26.0

∗ σ2s

–39.0

σ2s

π2p

–17.0 –19.5

z

O2

Fig. 3.3.3.

Energy level diagrams for N2 and O2 .

96

Fundamentals of Bonding Theory predicts that the ground electronic configuration of Ne2 (with two more electrons than F2 ) leads to a repulsive state. So far there is no experimental evidence for the existence of Ne2 , in agreement with molecular orbital results. 3.3.2

Heteronuclear diatomic molecules

(1) The hydrogen fluoride molecule Before discussing heteronuclear diatomic XY, where both X and Y are secondrow atoms, we first take HF as an example for detailed molecular orbital treatment. Since the H 1s orbital (with energy −13.6 eV) and F 2p (−17.4 eV) have similar energies, while that of F 2s (−37.8 eV) is much lower, we only need to consider the interaction between H 1s and F 2p orbitals. If we take the internuclear axis as the z axis, it is clear that the F 2pz and the H 1s orbital overlap. The bonding orbital (called σz ) is represent by the combination σz = c1 [1s(H)] + c2 [2pz (F)].

(3.3.2)

The coefficients c1 and c2 give the relative contributions of the H 1s and F 2pz orbitals to the σz orbital. Unlike the case of homonuclear diatomics, these coefficients are no longer equal, since the interacting atomic orbitals have different energies. As we know, bonding electrons are “pulled” toward the more electronegative atom, which has the more stable valence orbitals. Therefore, in eq. (3.3.2), c2 is greater than c1 ; i.e., the F 2pz contributes more than H 1s to the bonding molecular orbital σz . It is always true that the atomic orbital on the more electronegative atom contributes more to the bonding molecular orbital. The antibonding orbital (called σz∗ ) between F 2pz and H 1s orbitals has the form σz∗ = c3 [1s(H)] − c4 [2pz (F)].

H

HF

F σz∗

1s πxn πyn E

2p

σz 2s

Fig. 3.3.4.

Energy level diagram of HF.

2s

(3.3.3)

Since most of the 2pz orbital on F is “used up” in the formation of σz , it is now clear that, in σz∗ , c3 > c4 . In other words, the atomic orbital on the more electropositive atom always contributes more to the antibonding molecular orbital. The F 2px and F 2py orbitals are suitable for forming π molecular orbitals. However, in the HF molecule, the hydrogen 1s orbital does not have the proper symmetry to overlap with the F 2px or F 2py orbital. Thus, the F 2px and F 2py orbitals are nonbonding orbitals. By definition, a nonbonding molecular orbital in a diatomic molecule is simply an atomic orbital on one of the atoms; it gains or loses no stability (or energy) and its charge density is localized at the atom where the aforementioned atomic orbital originates. The energy level diagram for HF is shown in Fig. 3.3.4. By the dotted lines, we can see that σz is formed by the H 1s and F 2p (2pz in this case) orbitals. Since the energy of σz is closer to that of F 2p than that of H 1s, it is clear the F 2p orbital contributes more to the σz orbital. On the other hand, the H

Covalent Bonding in Molecules 1s contributes more to the σz∗ orbital. Also, the degenerate nonbonding πxn and πyn orbitals are formed solely by F 2px and F 2py orbitals, respectively, without any energy change. From the energy level diagram in Fig. 3.3.4, it follows naturally that the ground configuration of HF is 2s2 σz2 (πxn = πyn )4 . Among the four pairs of electron in this molecule, only the pair in σ z is shared by H and F, while the other three pairs are localized at F. This bonding picture is in total agreement with the Lewis formula: H F

Since the two electrons in σ z are not equally shared by H and F, it would be of interest to determine the charge separation in this molecule. This information is furnished by the experimentally determined dipole moment, 6.06 × 10−30 C m, of the molecule. Also, the electrons are closer to F than to H; i.e., the negative end of the dipole points toward F. The H–F bond length is 91.7 pm. If the lone electron of H is transferred to F, giving rise to the ionic structure H+ F− , the dipole moment would be (91.7 × 10−12 m) × (1.60 × 10−19 C) = 1.47 × 10−29 C m. Hence we see that the electron of H is only partially transferred to F. The ionic percentage of the HF may be estimated to be 6.06 × 10−30 C m × 100% = 41%. 1.47 × 10−29 C m (2) Heteronuclear diatomic molecules of the second-row elements Now we describe the bonding in a general diatomic molecule XY, where both X and Y are second-row elements and Y is more electronegative than X. The molecular orbital energy level diagram is shown in Fig. 3.3.5. The σ and π bonding and antibonding orbitals are formed in the same manner as for X2 , but the coefficients of the orbitals on Y are larger than those on X for the bonding orbitals, and the converse holds for the antibonding orbitals. In other words, the electrons in bonding orbitals are more likely to be found near the more electronegative atom Y, while the electrons in the antibonding orbitals are more likely to be near the more electropositive atom X. In Fig. 3.3.5, the molecular orbitals no longer carry the subscripts u and g, since there is no center of symmetry in XY. The bonding properties of several representative diatomics are discussed below. (a) BN (with eight valence electrons): This paramagnetic molecule has the ground configuration of 1σ 2 1σ *2 1π 3 2σ 1 , with two unpaired electrons. For this system, the 2σ orbital energy is higher than that of 1π by about the same energy required to pair two electrons. In any event, the bond order is 2. The bond lengths of C2 and BN are 124.4 and 128 pm, respectively. The

97

98

Fundamentals of Bonding Theory X

Y

XY 2σ ∗ 1π ∗

2p 2p 2σ 1π 1σ ∗

E 2s

2s

Fig. 3.3.5.

Energy level diagram of a heteronuclear diatomic molecule.

1σ

Fig. 3.3.6.

Energy level diagrams of CO and NO.

–14.0 –16.5 –19.7

–39.8

1π∗ 2σ

1π

1σ ∗

1σ CO

(b)

E (eV)

E (eV)

(a)

1π∗

–9.2 –14.6 –15.2

2σ

–23.4

1σ ∗

1π

1σ

–40.4 NO

bond energy of BN is 385 kJ mol−1 , suspiciously low compared with 602 kJ mol−1 for C2 . Clearly more experimental work is required in this case. (b) BO, CN, and CO+ (with nine valence electrons): The electronic configuration for these molecules is 1σ 2 1σ *2 1π 4 2σ 1 , with bond order 21/2. They all have bond lengths shorter than BN (or C2 ), 120 pm for BO, 117 pm for CN, and 112 pm for CO+ . Also, they have fairly similar bond energies: 800, 787, and 805 kJ mol−1 for BO, CN, and CO+ , respectively, all of which are greater than that of C2 . (c) NO+ , CO, and CN− (with ten valence electrons): Here the electronic configuration is 1σ 2 1σ *2 1π 4 2σ 2 , with a bond order of 3. They have similar bond lengths: 106, 113, and 114 pm for NO+ , CO, and CN− , respectively. The bond energy of carbon monoxide (1070 kJ mol−1 ) is slightly greater than that of N2 (941 kJ mol−1 ). The energy level diagram for CO is shown in Fig. 3.3.6(a). (d) NO (with eleven valence electrons): The ground electronic configuration is 1σ 2 2σ *2 1π 4 2σ 2z 1π*1 and the bond order is 21/2. The bond length of NO, 115 pm, is longer than those of both CO and NO+ . Its bond dissociation energy, 627.5 kJ mol−1 , is considerably less than those of CO and N2 . The importance of NO in both chemistry and biochemistry will be discussed

Covalent Bonding in Molecules

99

in detail in Section 14.2. The energy level diagram for NO is shown in Fig. 3.3.6(b). 3.4

Linear triatomic molecules and spn hybridization schemes

In this section, we first discuss the bonding in two linear triatomic molecules: BeH2 with only σ bonds and CO2 with both σ and π bonds. Then we go on to treat other polyatomic molecules with the hybridization theory. Next we discuss the derivation of a self-consistent set of covalent radii for the atoms. Finally, we study the bonding and reactivity of conjugated polyenes by applying Hückel molecular orbital theory. 3.4.1

Beryllium hydride, BeH2

The molecular orbitals of this molecule are formed by the 2s and 2p orbitals of Be and the 1s orbitals of Ha and Hb . Here we take the molecular axis in BeH2 as the z axis, as shown in Fig. 3.4.1. To form the molecular orbitals for polyatomic molecules AXn , we first carry out linear combinations of the orbitals on X and then match them, taking into account their symmetry characteristics, with the atomic orbitals on the central atom A. For our simple example of BeH2 , the valence orbitals on Ha and Hb , 1sa and 1sb , can form only two linear (and independent) combinations: 1sa + 1sb and 1sa − 1sb . We can see that combination 1sa + 1sb matches in symmetry with the Be 2s orbital. Hence they can form both bonding and antibonding molecular orbitals: σs = c1 2s(Be) + c2 (1sa + 1sb ),

σs∗

=

c1, 2s(Be) − c2, (1sa

+ 1sb ),

c2 > c1

(3.4.1)

c1,

(3.4.2)

>

c2, .

The relative magnitudes of coefficients c1 and c2 , as well as those of c1, and c2, , are determined by the relative electronegatives of the atoms concerned, which are reflected by the relative energies of the atomic orbitals. Similarly, the combination 1sa − 1sb has a net overlap with the 2pz orbital of Be. They form bonding and antibonding molecular orbitals in the following manner: σz = c3 2pz (Be) + c4 (1sa − 1sb ),

σz∗

=

c3, 2pz (Be) − c4, (1sa

− 1sb ),

c4 > c3

(3.4.3)

c3,

(3.4.4)

>

c4, .

Finally, the 2px and 2py orbitals on Be are not symmetry-compatible with the 1sa or 1sb orbitals (or their linear combinations). Hence they are nonbonding orbitals: ) n πx = 2px (Be) . (3.4.5) πyn = 2py (Be)

y

z

Ha

Be

x Fig. 3.4.1.

Coordinate system for BeH2 .

Hb

100

Fundamentals of Bonding Theory Table 3.4.1. Summary of the formation of the molecular orbitals in BeH2

Orbital on Be 2s D2pz 2px 2py

Be

BeH2

2H

σz* σs* πxn

2p

πyn

E

2s

σz σs Fig. 3.4.2.

Energy level diagram of BeH2 .

1sa 1sb

Orbitals on H

Molecular orbitals

1 (2)− /2 (1sa + 1sb ) 1 − (2) /2 (1sa − 1sb )

σs , σs∗ ∗ Dσz , σz n πx πyn

—

There are totally six molecular orbitals (σs , σs∗ , σz , σz∗ , πxn , and πyn ) formed by the six atomic orbitals (2s and 2p orbitals on Be and 1s orbitals on the hydrogens). Note that the σ molecular orbitals have cylindrical symmetry around the molecular axis, while the nonbonding π orbitals do not. Another important characteristic of these orbitals is that they are “delocalized“ in nature. For example, an electron occupying the σs orbital has its density spread over all three atoms. Table 3.4.1 summarizes the way the molecular orbitals of BeH2 are formed by the atomic orbitals on Be and H, where the linear combinations of H orbitals are normalized. The energy level diagram for BeH2 , shown in Fig. 3.4.2, is constructed as follows. The 2s and 2p of Be are shown on the left of the diagram, while the 1s orbitals of the hydrogens are shown on the right. Note that the H 1s orbitals are placed lower than either the Be 2p or Be 2s orbitals. This is because Be is more electropositive than H. The molecular orbitals—bonding, antibonding, and nonbonding—are placed in the middle of the diagram. As usual, the bonding orbitals have lower energy than the constituent atomic orbitals, and correspondingly the antibonding orbitals are of higher energy. The nonbonding orbitals have the same energy as their parent atomic orbitals. After constructing the energy level diagram, we place the four valence electrons of BeH2 in the two lowest molecular orbitals, leading to a ground electronic configuration of σs2 σz2 . In this description, the two electron-pair bonds are spread over all these atoms. The delocalization of electrons is an important feature of the molecular orbital model. Concluding the molecular orbital treatment of BeH2 , we can see that the two (filled) bonding molecular orbitals σs and σz have different shapes and different energies. This is contrary to our intuition for BeH2 : we expect the two bonds in BeH2 to be identical (in shape as well as in stability) to each other. In any event, this is the picture provided by the molecular orbital model. 3.4.2

Hybridization scheme for linear triatomic molecules

If we prefer to describe the bonding of a polyatomic molecule using localized two-center, two-electron (2c-2e) bonds, we can turn to the hybridization theory, which is an integral part of the valence bond method. In this model, for AXn systems, we linearly combine the atomic orbitals on atom A in such a way that the resultant combinations (called hybrid orbitals) point toward the X atoms. For our BeH2 molecule in hand, two equivalent, colinear hybrid orbitals are constructed from the 2s and 2pz orbitals on Be, which can overlap with the two 1s hydrogen orbitals to form two Be–H single bonds. (The 2px and 2py

Covalent Bonding in Molecules

101

(a)

+

z

+

h1

(b) –

Be –

+ z

Be –

z

+ z

Be +

– Be + h2

(c) +

Be + – – +

Ha

Fig. 3.4.3.

+

The formation of the two sp hybrid orbitals in BeH2 [(a) and (b)] and the two equivalent bonds in BeH2 (c).

Hb

orbitals do not take part in the hybridization scheme, otherwise the resultant hybrid orbitals would not point directly at the hydrogens.) If we combine the 2s and 2pz orbitals in the following manner: −1 h1 = (2) /2 (2s + 2pz ),

(3.4.6)

h2 = (2)

(3.4.7)

− 1/2

(2s − 2pz ),

the hybrid orbitals h1 and h2 would overlap nicely with the 1s orbitals on Ha and Hb , respectively, as shown in Fig. 3.4.3. The two bonding orbitals in BeH2 have the wavefunctions ψ1 = c5 h1 + c6 1sa , ψ2 = c5 h2 + c6 1sb ,

c6 > c5

(3.4.8)

c6 > c5 .

(3.4.9)

So now we have two equivalent bonding orbitals ψ1 and ψ2 with the same energy. Moreover, ψ1 and ψ2 are localized orbitals: ψ1 is localized between Be and Ha and ψ2 between Be and Hb . They are 2c-2e bonds. y

3.4.3

ya

Carbon dioxide, CO2

Carbon dioxide is a linear molecule with both σ and π bonds. The coordinate system chosen for CO2 is shown in Fig. 3.4.4. Once again, the molecular axis is taken to be the z axis. The atomic orbitals taking part in the bonding of this molecule are the 2s and 2p orbitals on C and the 2p orbitals on O. There are a total of ten atomic orbitals and they will form ten molecular orbitals. The σ orbitals in CO2 are very similar to those in BeH2 . The only difference is that the oxygens make use of their 2pz orbitals instead of the 1s orbitals used

z

Oa

xa x

yb za

zb

C xb

Fig. 3.4.4.

The coordinate system of CO2 .

Ob

102

Fundamentals of Bonding Theory (a)

(b) xa

+xa

Fig. 3.4.5.

(a) The linear combination (xa + xb ), which overlaps with the 2px orbital on C, and (b) linear combination (xa − xb ), which does not overlap with the 2px orbital on C. Here xa and xb represent 2px (a) and 2px (b), respectively.

+x

x

xb

+

+

+

–

–

–

no net overlap xb x xa +xa +x –xb – + +

+xb z

–

–

+

z

no net overlap

by the hydrogens in BeH2 . The σ orbitals thus have the wavefunctions σs = c7 2s(C) + c8 [2pz (a) + 2pz (b)],

σs∗

=

c7, 2s(C) − c8, [2pz (a) + 2pz (b)],

=

, c9, 2pz (C) − c10 [2pz (a) + 2pz (b)],

c7 > c8

(3.4.10)

c8,

(3.4.11)

σz = c9 2pz (C) + c10 [2pz (a) + 2pz (b)],

σz∗

>

c7,

c10 > c9

(3.4.12)

c9,

(3.4.13)

>

, c10 .

The π molecular orbitals are made up of the 2px and 2py orbitals of the three atoms. Let’s take the 2px orbitals first. The two 2px orbitals can be combined in two ways: 2px (a) + 2px (b)

(3.4.14)

2px (a) − 2px (b).

(3.4.15)

Combination (3.4.14) overlaps with the C 2px orbital as shown in Fig. 3.4.5(a). Since, for our linear molecule, the x and y axes are equivalent (and not uniquely defined), we can readily write down the following π bonding and antibonding molecular orbitals: πx = c11 2px (C) + c12 [2px (a) + 2px (b)],

πx∗

c12 > c11

(3.4.16)

=

, , c11 2px (C) − c12 [2px (a) + 2px (b)],

, c11

, c12

(3.4.17)

c12 > c11

(3.4.18)

=

, , c11 2py (C) − c12 [2px (a) + 2px (b)],

, c11

(3.4.19)

πy = c11 2py (C) + c12 [2py (a) + 2py (b)],

πy∗

>

>

, c12

On the other hand, combination (3.4.15) has zero overlap with the C 2px orbital [Fig. 3.4.5(b)] and is therefore a nonbonding orbital. Indeed, we have two equivalent nonbonding orbitals: πxn = 2px (a) − 2px (b)

πyn

= 2py (a) − 2py (b).

(3.4.20) (3.4.21)

As previously mentioned, ten molecular orbitals are formed. Table 3.4.2 summarizes the formation of the molecular orbitals in CO2 , where the linear combinations of O orbitals are normalized. Note that all bonding and antibonding orbitals spread over all three atoms, while the nonbonding orbitals have no participation from C orbitals.

Covalent Bonding in Molecules

103

Table 3.4.2. Summary of the formation of the molecular orbitals in CO2

Orbitals on O∗

Orbital on C

Molecular orbitals

1 (2) /2 (za + zb ) 1 (2) /2 (za − zb ) 1 E(2)1/2 (xa + xb ) (2) /2 (ya + yb ) E(2)1/2 (xa − xb ) 1 (2) /2 (y − y )

2s 2pz E2px 2py

a

b

σs , σs∗ σz , σz∗ E πx E πx∗ πy πy∗

Eπxn πyn

∗ Here x represents 2p (a), Similar abbreviations are also used to designate a x other orbitals on the oxygen atoms.

C

CO2

2O

σz* σs*

2p

πx*

πy*

π xn

π yn

πx

πy

E

2pa 2pb

2s

σz σs 2sa

2sb

2sa 2sb

The energy level diagram for CO2 is shown in Fig. 3.4.6. Note that the oxygen 2p orbitals are more stable than their corresponding orbitals on carbon. The 16 valence electrons in CO2 occupy the orbitals as shown in Fig. 3.4.6 and the ground configuration for CO2 is 2s2a 2s2b σs2 σz2 (πx = πy )4 (πxn = πyn )4 . So there are two σ bonds, two π bonds, and four nonbonding electron pairs localized on the oxygen atoms. In the valence bond or hybridization model for CO2 , we have two resonance (or canonical) structures, as shown in Fig. 3.4.7. In both structures, the two σ bonds are formed by the sp hybrids on carbon with the 2pz orbitals on the oxygens. In the left resonance structure, the π bonds are formed by the 2px orbitals on C and Oa and the 2py orbitals on C and Ob . In the other structure, the π bonds are formed by the 2px orbitals on C and Ob and the 2py orbitals on C and Oa . The “real” structure is a resonance hybrid of these two extremes. In effect, once again, we get two σ bonds, two π bonds, and four “lone pairs” on the two oxygens. This description is in total agreement with the molecular orbital picture. The only difference is that electron delocalization in CO2 is

Fig. 3.4.6.

Energy level diagram of CO2 .

104

Fundamentals of Bonding Theory x

x

x

x

x

x

π

π 2s

za

y

spa

spb

σ

σz

b

2s

2s

π

y

za

σ spa

σ spb

zb

2s

π

y

y

y

y

Fig. 3.4.7.

The resonance structures of CO2 .

inherent in the molecular orbital model, whereas description according to the valence-bond hybridization scheme requires the concept of resonance between two canonical structures. 3.4.4

The spn (n = 1–3) hybrid orbitals

(1) The sp hybridization scheme Recalling from Section 3.4.1, we use the s orbital and the pz orbital to form two equivalent hybrid orbitals, one pointing in the +z direction and the other in the −z direction. These two orbitals are called sp hybrids, since they are formed by one s and one p orbital. The wavefunctions of the sp hybrid orbitals are given by eqs. (3.4.6) and (3.4.7). In matrix form the wavefunction are , , ,, , , , ,, , 1 , h1 , , 1/(2)1/2 1/(2) /2 ,, ,, s ,, ,, a b ,, ,, s ,, ,=, , (3.4.22) , h2 , , 1/(2)1/2 −1/(2)1/2 , , pz , = , c d , , pz ,

We now use this 2 × 2 coefficient matrix to illustrate the relationships among the coefficients: (a) Since each atomic orbital is “used up” in the construction of the hybrids, a2 + c2 = 1 and b2 + d 2 = 1. (b) Since each hybrids is normalized, a2 + b2 = 1 and c2 + d 2 = 1. (c) Since hybrids are orthogonal to each other, ac + bd = 0.

h3

+ –

h1

+

– –

h2 y

+ x

Fig. 3.4.8.

A coordinate system for the sp2 hybrid orbitals.

(2) The sp2 hybridization scheme If we use the s orbital and the px and py orbitals to form three equivalent orbitals h1 , h2 , and h3 , these orbitals are called sp2 hybrids. Furthermore, they lie in the xy plane and form 120◦ angles between them. Now the hybrids have the wavefunctions , , ,, , , , h1 , , a b c , , s , , , ,, , , , h2 , = , d e f , , px , . (3.4.23) , , ,, , , , h3 , , g j k , , py ,

If the three hybrids have the orientations as shown in Fig. 3.4.8, we then get the following results for the coefficients. Since the s orbital is (equally) split among the three equivalent hybrids, a2 = d 2 = g 2 = 1/3, 1/2

a = d = g = 1/(3)

.

(3.4.24) (3.4.25)

Covalent Bonding in Molecules (a) Since h1 lies on the x axis, py cannot contribute to h1 , c = 0.

(3.4.26)

(b) Relation a2 + b2 + c2 = 1 leads to # $1/2 2 b= . 3

(3.4.27)

(c) Orbital px contributes equally to h2 and h3 and b2 + e2 + j 2 = 1. Hence # $1/2 1 . e=j=− 6

(3.4.28)

Note that both e and j are negative because h2 and h3 project on the −x direction. (d) Orbital py contributes equally to h2 and h3 (but f > 0 and k < 0) and c2 + f 2 + k 2 = 1. Hence 1 f = 1/(2) /2 ,

(3.4.29)

1 k = −1/(2) /2 .

(3.4.30)

Collecting all the coefficients, we have , , , 1 , h1 , ,, 1/(3) /2 , , , , h2 , = , 1/(3)1/2 , , , h3 , ,, 1 1/(3) /2

1

(2/3) /2 1 −1/(6) /2 1 −1/(6) /2

0 1 1/(2) /2 1 −1/(2) /2

,, ,, ,, s ,, , , px ,, , py

, , , ,. , ,

(3.4.31)

The correctness of these coefficients can be checked in many ways. For example, C . # $1/2 B 1 1 2 − 1 +0 − 1 = 0. + ad + be + cf = 1 1 3 (3) /2 (3) /2 (6) /2 (2) /2 (3.4.32) 1

1

Also, the angle θ between h2 and the +y axis can be calculated: −1 −1 −1 θ = tan−1 [(6) /2 /(2) /2 ] = tan−1 (3) /2 = 30◦ .

(3.4.33)

To confirm that h1 , h2 , and h3 are equivalent to each other, we can calculate their hybridization indices and see that they are identical. The hybridization index n of a hybrid orbital is defined as m=

total p orbital population = total s orbital population

|p orbital coefficients|2 . |s orbital coefficients|2


.. . D∞h A1g ≡ ∞ 1 1 2 cos > 2 cos 2> 2 cos 3> .. . 2C > ∞ 1 1 2 cos > 2 cos 2> ··· 1 1 2 cos > 2 cos 2> 2 cos 3> .. .

· · ·∞σ v ··· 1 · · · −1 ··· 0 ··· 0 ··· 0 .. .. . . · · ·∞σ v ··· 1 · · · −1 ··· 0 ··· 0 ··· ··· ··· 1 · · · −1 ··· 0 ··· 0 ··· 0 .. .. . .

z Rz (x, y)(Rx , Ry )

i 1 1 2 2 ··· −1 −1 −2 −2 −2 .. .

x2 + y2 , z 2

z3

(xz, yz) (x2 − y2 , xy)

(xz 2 , yz 2 ) [xyz, z(x2 − y2 )] [x(x2 − 3y2 ), y(3x2 − y2 )]

2S > ∞ 1 1 −2 cos > 2 cos 2> ··· −1 −1 2 cos > −2 cos 2> 2 cos 3> .. .

· · ·∞C 2 ··· 1 · · · −1 ··· 0 ··· 0 ··· ··· · · · −1 ··· 1 ··· 0 ··· 0 ··· 0 .. .. . .

Rz (Rx , Ry )

x2 + y2 , z 2 (xz, yz) (x2 − y2 , xy)

z

z3

(x, y)

(xz 2 , yz 2 ) [xyz, z(x2 − y2 )] [x(x2 − 3y2 ), y(3x2 − y2 )]

11. The Icosahedral groups 12C 5 1 η+ η− −1 0

12C 25 1 η− η+ −1 0

20C 3 1 0 0 1 −1

I A T1 T2 G H

E 1 3 3 4 5

Ih Ag T1g T2g Gg Hg

E 1 3 3 4 5

12C 5 1 η+ η− −1 0

12C 25 1 η− η+ −1 0

Au T1u T2u

1 3 3

1 η+ η−

1 η− η+

1 0 0

Gu

4

−1

−1

1

Hu

5

0

0

−1

20C 3 1 0 0 1 −1

15C 2 1 −1 −1 0 1

(x, y, z)(Rx , Ry , Rz )

η± = 1/2[1 ± (5)1/2 ] x2 + y2 + z 2

(2z 2 − x2 − y2 , x2 − y2 , xy, xz, yz)

15C 2 1 −1 −1 0 1

i 1 3 3 4 5

12S 10 1 η− η+ −1 0

12S 310 1 η+ η− −1 0

20S 6 1 0 0 1 −1

15σ 1 −1 −1 0 1

(Rx , Ry , Rz )

1 −1 −1

−1 −3 −3

−1 −η− −η+

−1 −η+ −η−

−1 0 0

−1 1 1

(x, y, z)

1

−1

0

1

−5

0

1

−1

0

−4

1 0

x2

η± = 1/2[1 ± (5)1/2 ] + y2 + z 2

(2z 2 − x2 − y2 , x2 −y2 , xy, xz, yz)

Note: In these groups and others containing C5 , the following relationships may be useful: η+ = 1/2[1 + (5)1/2 ] = 1.61803 . . . = −2 cos 144◦ η− = 1/2[1 − (5)1/2 ] = −0.61803 . . . = −2 cos 72◦ η+ × η+ = 1 + η+ , η− × η− = 1 + η− , η+ × η− = −1.

(x3 , y3 , z 3 ) [x(z 2 − y2 ), y(z 2 − x2 ), z(x2 − y2 ), xyz]

(x3 , y3 , z 3 ) [x(z 2 − y2 ), y(z 2 − x2 ), z(x2 − y2 ), xyz]

7

Application of Group Theory to Molecular Systems In this chapter, we discuss the various applications of group theory to chemical problems. These include the description of structure and bonding based on hybridization and molecular orbital theories, selection rules in infrared and Raman spectroscopy, and symmetry of molecular vibrations. As will be seen, even though most of the arguments used are qualitative in nature, meaningful results and conclusions can be obtained. 7.1

Molecular orbital theory

As mentioned previously in Chapter 3, when we treat the bonding of a molecule by applying molecular orbital theory, we need to solve the secular determinant , , H11 − ES11 , , H12 − ES12 , , .. , . , , H1n − ES1n

H12 − ES12 H22 − ES22 .. .

. . . H1n − ES1n . . . H2n − ES2n .. .

H2n − ES2n

. . . Hnn − ESnn

, , , , , , = 0. , , ,

(7.1.1)

In eq. (7.1.1), energy E is the only unknown, while energy interaction integrals Hij (≡ ∫ φi Hˆ φj dτ ) and overlap integrals Sij (≡ ∫ φi φj d τ ) are calculated with known atomic orbitals φ1 , φ2 , . . . φn . After solving for E (n of them in all), we can substitute each E in the following secular equations to determine the values of coefficients ci :  (H11 − ES11 )c1 + (H12 − ES12 )c2 + . . . + (H1n − ES1n )cn = 0     (H12 − ES12 )c1 + (H22 − ES22 )c2 + . . . + (H2n − ES2n )cn = 0 .. .. .. .. .  . . . .    (H1n − ES1n )c1 + (H2n − ES2n )c2 + . . . + (Hnn − ESnn )cn = 0 (7.1.2) In molecular orbital theory, the molecular orbitals are expressed as linear combinations of atomic orbitals: ψ=

n 9 i=1

ci φi = c1 φ1 + c2 φ2 + . . . + cn φn .

(7.1.3)

214

Symmetry in Chemistry So we have n E’s from eq. (7.1.1), and each E value leads to a set of coefficients, or to one molecular orbital. In other words, n atomic orbitals form n molecular orbitals; i.e., the number of orbitals is conserved. The solution of eq. (7.1.1) is made easier if the secular determinant can be put in block-diagonal form, or block-factored: n zeroes

k%k l%l

n zeroes

# k % k % l % l % . . . % m % m # 0, with k ! l ! ... ! m # n.

m%m

(7.1.4)

We will then be solving several small determinants (k × k; l × l; . . .; m × m) instead of a very large one (n × n). By taking advantage of the symmetry property of the system, group theory can do just that. In this section, we illustrate the reduction of the secular determinant by studying several representative molecular systems. z

7.1.1

Hb

Ha y O

Fig. 7.1.1.

Coordinate system for the H2 O molecule. Note that the x axis points toward the reader.

AHn (n = 2–6) molecules

As mentioned in Chapter 3, to construct the molecular orbitals for an AXn molecule, we need to combine the atomic orbitals on X and then match the resultant combinations with the atomic orbitals on the central atom A. With group theory, we can derive the linear combinations systematically. Let us use the simple molecule H2 O as the first example. The coordinate system we adopt for this molecule is shown in Fig. 7.1.1. The orientation of the adopted set of axes is similar to that for H2 S in Fig. 6.4.2. If we assume that the 2s and 2p orbitals of oxygen and the 1s orbitals of the hydrogen atoms take part in the bonding, the secular determinant to be solved has the dimensions 6 × 6. Now we proceed to determine the symmetries of the participating atomic orbitals. From the C2v character table, it can be seen that the 2px , 2py , and 2pz orbitals on oxygen have B1 , B2 , and A1 symmetries, respectively, while the oxygen 2s orbital, being totally symmetric, has A1 symmetry. To determine the characters of the representation generated by the hydrogen 1s orbitals, we make use of this simple rule: the character (of an operation) is equal to the number of objects (vectors or orbitals) unshifted by the operation. So, for the hydrogen 1s orbitals: C2v ΓH

E 2

C2 0

σ v (xz) 0

σ ,v (yz) 2

≡ A1 + B2

In other words, the two 1s orbitals will form two linear combinations, one with A1 symmetry and the other with B2 symmetry. To deduce these two linear combinations, we need to employ the projection operator, which is defined as Pi =

h 9 j=1

χ i (R j )R j ,

(7.1.5)

Application of Group Theory to Molecular Systems where P i is the projection operator for representation Γi , χ i (R j ) is the character of the representation Γi for operation R j , and the summation is over all the symmetry operations (h in total). To derive the linear combinations of the hydrogen 1s orbitals with A1 symmetry, we apply P A1 on, say, the 1s orbital on Ha (denoted as 1sa ). So we need to know the result of applying every symmetry operation in the C2v group to 1sa : C2v 1sa

E 1sa

C2 1sb

σ v (xz) 1sb

σ ,v (yz) 1sa

Now we apply P A1 to 1sa : P A1 (1sa ) = [1 · E + 1 · C 2 + 1 · σ v (xz) + 1 · σ ,v (yz)]1sa = 1sa + 1sb + 1sb + 1sa = 2(1sa ) + 2(1sb )

⇒ (2)−1/2 (1sa + 1sb ) (after normalization).

(7.1.6)

To obtain the combination with B2 symmetry: P B2 (1sa ) = [1 · E + (−1)C 2 + (−1)σ v (xz) + 1 · σ ,v (yz)]1sa = 1sa − 1sb − 1sb + 1sa = 2(1sa ) − 2(1sb )

⇒ (2)−1/2 (1sa − 1sb ) (after normalization).

(7.1.7)

In Table 7.1.1 we summarize the way in which the molecular orbitals are formed in H2 O. From these results, we can see that the original 6×6 secular determinant is now block-factored into three smaller ones: one 3×3 for functions with A1 symmetry, one 2×2 with B2 symmetry, and one 1×1 with B1 symmetry. A schematic energy diagram for this molecule is shown in Fig. 7.1.2. From this diagram, we can see that there are two bonding orbtals (1a1 and 1b2 ), two other orbitals essentially nonbonding (2a1 and 1b1 ), and two antibonding orbitals (2b2 and 3a1 ). Also, all the bonding and nonbonding orbitals are filled, giving rise to a ground electronic configuration of (1a1 )2 (1b2 )2 (2a1 )2 (1b1 )2 and an electronic state of 1 A1 . This bonding picture indicates that H2 O has two σ bonds and two filled nonbonding orbitals. Such a result is in qualitative agreement with the familiar valence bond description for this molecule. In passing, it is of interest to note that, according to Fig. 7.1.2, the first excited electronic configuration is (1a1 )2 (1b2 )2 (2a1 )2 (1b1 )1 (2b2 )1 , giving rise to states 3 A2 and 1 A2 . It is easy to show that electronic transition A1 → A2 is not allowed for a molecule with C2v symmetry. In other words, 1 A1 → 1 A2 Table 7.1.1. Formation of the molecular orbitals in H2 O

Symmetry

Orbital on O

Orbitals on H

Molecular orbitals

A1

2s 2pz 2px 2py

(2)1/2 (1sa + 1sb )

1a1 , 2a1 , 3a1

— (2)1/2 (1sa − 1sb )

1b1 1b2 , 2b2

B1 B2

215

216

Symmetry in Chemistry 3a1 2b2

E

1sa

2p

1sb

1b1 2a1

2s 1b2 1a1

Fig. 7.1.2.

A schematic energy level diagram for H2 O.

O

y Hb

x B

Ha

Hc

H

H2O

is spin-allowed and symmetry-forbidden, while 1 A1 →3A2 is both spin- and symmetry-forbidden. Now let us turn to a slightly more complicated system, that of BH3 with D3h symmetry. Note that BH3 is not a stable species: it dimerizes spontaneously to form diborane, B2 H6 . A convenient coordinate system for BH3 is shown in Fig. 7.1.3. From the D3h character table, it is readily seen that boron 2s and 2pz orbitals have A,1 and A,,2 symmetry, respectively, while the 2px and 2py orbitals form an E , set. To determine the symmetry species of the hydrogen 1s orbital combinations, we perform the operations

Fig. 7.1.3.

D3h ΓH

Coordinate system for BH3 .

E 3

2C 3 0

3C 2 1

σh 3

2S 3 0

3σ v 1

≡ A,1 + E ,

So, among the three linear combinations of hydrogen 1s orbitals, one has A,1 symmetry, while the remaining two form an E , set. To obtain the explicit functions, we require the symmetry operation results D3h 1sa

E 1sa

2C 3 1sb , 1sc

3C 2 1sa , 1sb , 1sc

2S 3 1sb , 1sc

σh 1sa

3σ v 1sa , 1sb , 1sc

Now, it is straightforward to obtain the linear combinations ,

P A1 (1sa ) = 1(1sa ) + 1(1sb + 1sc ) + 1(1sa + 1sb + 1sc ) + 1(1sa ) + 1(1sb + 1sc ) + 1(1sa + 1sb + 1sc )

= 4(1sa + 1sb + 1sc ) E,

⇒ (3)−1/2 (1sa + 1sb + 1sc )

(after normalization);

(7.1.8)

P (1sa ) = 2(1sa ) − 1(1sb + 1sc ) + 2(1sa ) − 1(1sb + 1sc ) = 4(1sa ) − 2(1sb + 1sc )

⇒ (6)−1/2 [2(1sa ) − 1sb − 1sc ]

(after normalization). (7.1.9)

Application of Group Theory to Molecular Systems

217

Still one more combination is required to complete the E , set. It is not difficult , to see that when we operate P E on 1sb and 1sc , we get ,

P E (1sb ) = (6)−1/2 [2(1sb ) − 1sa − 1sc ],

(7.1.10)

,

P E (1sc ) = (6)−1/2 [2(1sc ) − 1sa − 1sb ].

(7.1.11)

Since the two combinations of an E , set must be linearly independent, and summation of eqs. (7.1.10) and (7.1.11) yield eq. (7.1.9) (aside from a normalization factor), we need to take the difference of eqs. (7.1.10) and (7.1.11) to obtain the remaining combination: [2(1sb ) − 1sa − 1sc ] − [2(1sc ) − 1sa − 1sb ] = 3(1sb − 1sc ) ⇒ (2)−1/2 (1sb − 1sc )

[after normalization].

(7.1.12)

Obviously, there are different ways to choose the combination of an E , set. We choose the ones given by eqs. (7.1.9) and (7.1.12) because these functions overlap with the boron 2px and 2py orbitals, respectively, as shown in Fig. 7.1.4. Table 7.1.2 summarizes how the molecular orbitals in BH3 are formed. From these results, we can see that the original 7×7 secular determinant (four orbitals from B and three from the H’s) is block-factored into three 2×2 and one 1×1 determinants. The 1×1 has A,,2 symmetry, one 2×2 has A,1 symmetry, while the remaining two 2×2 form an E , set. It is important to note that the two 2×2 determinants that form the E , pair have the same pair of roots; i.e., we only need to solve one of these two determinants! A schematic energy level diagram for BH3 is shown in Fig. 7.1.5. According to this diagram, the ground configuration for BH3 is (1a1, )2 (1e, )4 and the ground state is 1 A,1 . y

y

(a) –

(b)

Hb

Hb +

Fig. 7.1.4.

+ –

+

+ Ha

Ha

x

x

–

– Hc

– Hc

Table 7.1.2. Summary of the formation of the molecular orbitals in BH3

Symmetry

Orbital on B

Orbitals on H

Molecular orbitals

A,1

2s )

(3)−1/2 (1sa + 1sb + 1sc ) ) (6)−1/2 [2(1sa ) − 1sb − 1sc ] (2)−1/2 (1sb − 1sc ) —

1a1, , 2a1,

E, A,,2

2px 2py 2pz

1e, , 2e, 1a2,,

(a) Overlap between the boron 2px orbital with combination (6)−1/2 [2(1sa ) − 1sb − 1sc ]. (b) Overlap between the boron 2py orbital with the combination (2)−1/2 [1sb − 1sc ]. By symmetry, the total overlaps in (a) and (b) are the same.

218

Symmetry in Chemistry 2e& 2a1&

E 2p

1a2''

1sb

1sc

1e'

2s 1a1'

Fig. 7.1.5.

A schematic energy level diagram for BH3 .

z Hb Ha C

y

B

H

BH3

Next we turn to the highly symmetric molecule CH4 , which belongs to point group Td . A coordinate system for this molecule is shown in Fig. 7.1.6. For this molecule, there are eight valence atomic orbitals: 2s and 2p orbitals of carbon and the 1s orbitals of the hydrogens. Regarding the carbon orbitals, 2s has A1 symmetry, while the 2px , 2py , and 2pz orbitals form a T2 set. The irreducible representations spanned by the hydrogen 1s orbitals can be readily determined: Td ΓH

Hd x

1sa

E 4

8C 3 1

3C 2 0

6S 4 0

6σ d 2

Hc

Fig. 7.1.6.

Coordinate system for CH4 .

≡ A1 + T2

So the four hydrogen 1s orbitals form one linear combination with A1 symmetry and three other combinations that make up a T2 set. To obtain these combinations, we make use of the symmetry operation results Td 1sa

E 1sa

8C 3 3C 2 2(1sa ), 2(1sb ), 1sb , 1sc , 2(1sc ), 2(1sd ) 1sd

6S 4 2(1sb ), 2(1sc ), 2(1sd )

6σ d 3(1sa ), 1sb , 1sc , 1sd

Now the linear combination can be obtained readily: P A1 (1sa ) = 1(1sa ) + 1[2(1sa ) + 2(1sb ) + 2(1sc ) + 2(1sd )]

+ 1(1sb + 1sc + 1sd ) + 1[2(1sb ) + 2(1sc ) + 2(1sd )] + 1[3(1sa ) + 1sb + 1sc + 1sd ] ⇒

1 (1sa + 1sb + 1sc + 1sd ) 2

(after normalization). (7.1.13)

T2

P (1sa ) = 3(1sa ) − 1(1sb + 1sc + 1sd ) − 1[2(1sb ) + 2(1sc ) + 2(1sd )] + 1[3(1sa ) + 1sb + 1sc + 1sd ]

= 6(1sa ) − 2(1sb ) − 2(1sc ) − 2(1sd ).

(7.1.14)

Application of Group Theory to Molecular Systems

219

Similarly, when we operate P T2 on 1sb , 1sc , 1sd , we obtain P T2 (1sb ) = 6(1sb ) − 2(1sa ) − 2(1sc ) − 2(1sd ),

(7.1.15)

P T2 (1sc ) = 6(1sc ) − 2(1sa ) − 2(1sb ) − 2(1sd ),

(7.1.16)

P (1sd ) = 6(1sd ) − 2(1sa ) − 2(1sb ) − 2(1sc ).

(7.1.17)

T2

To obtain the three linear combinations of the T2 set, we combine eqs. (7.1.14) to (7.1.17) in the following manner: Sum of eqs. (7.1.14) and (7.1.15): 1 (1sa + 1sb − 1sc − 1sd ) 2 (after normalization). (7.1.18)

4(1sa ) + 4(1sb ) − 4(1sc ) − 4(1sd ) =

1 (1sa − 1sb + 1sc − 1sd ). 2 1 Sum of eqs. (7.1.14) and (7.1.17) : (1sa − 1sb − 1sc + 1sd ). 2

Sum of eqs. (7.1.14) and (7.1.16) :

(7.1.19) (7.1.20)

There are many ways of combining eqs. (7.1.14) to (7.1.17) to arrive at the three combinations that form the T2 set. We choose those ones given by eqs. (7.1.18) to (7.1.20) as these functions overlap effectively with the 2pz , 2px , and 2py orbitals, respectively, as shown in Fig. 7.1.7. Table 7.1.3 summarizes the formation of the molecular orbitals in CH4 . For this molecule, the original 8×8 secular determinants is reduced to four 2×2 ones, one with A1 symmetry, while the other three form a T2 set. In other words, we only need to solve the A1 2×2 determinant as well as one of the three determinants that form the T2 set. By symmetry, the three determinants z

z

z

–

–

+ +

+

+

+

–

y

+

y

–

– x

y

+ +

–

+ x

–

– – x

Table 7.1.3. Formation of the molecular orbitals in CH4

Symmetry

Orbital on C

Orbitals on H

Molecular orbitals

A1

2s

1 (1s + 1s + 1s + 1s ) a c b d 2  1  (1s − 1sb + 1sc − 1sd )   2 a 1 (1s − 1s − 1s + 1s ) a c b d 2    1 2 (1sa + 1sb − 1sc − 1sd )

1a1 , 2a1

T2

  2px 2py  2pz

1t2 , 2t2

Fig. 7.1.7.

The overlap between 2px , 2pz , and 2py orbitals of carbon with the 1s orbitals of the hydrogens in CH4

220

Symmetry in Chemistry 2t2 2a1

E 2p

1s 2s 1t2 1a1

Fig. 7.1.8.

A schematic energy level diagram for CH4 .

C

CH4

H

Table 7.1.4. Formation of the molecular orbitals in AH5

Symmetry Orbital on A Orbitals on H A,1 E, A,,2

z Ha He

Hd

A

y

Hc

x

Hb

Fig. 7.1.9.

Coordinate system for AH5 .

z He Hd

Hb

A x

Ha

Hc Hf

Fig. 7.1.10.

Coordinate system for AH6 .

y

ns )

npx npy

npz

(2)−1/2 (1sa + 1sb ) (3)−1/2 (1sc + 1sd + 1se ) ) (6)−1/2 [2(1sc ) − 1sd − 1se )] (2)−1/2 (1sd − 1se ) (2)−1/2 (1sa − 1sb )

Molecular Orbitals 1a1, , 2a1, , 3a1, 1e, , 2e, 1a2,, , 2a2,,

forming the T2 set have the same roots. A schematic energy level diagram for CH4 is shown in Fig. 7.1.8. According to this diagram, the ground configuration is simply (1a1 )2 (1t2 )6 and the ground state is 1 A1 . So far we have illustrated the method for constructing the linear combinations of atomic orbitals, using H2 O, BH3 , and CH4 as examples. In these simple systems, all the ligand orbitals are equivalent to each other. For molecules with non-equivalent ligand sites, we first linearly combine the orbitals on the equivalent atoms. Then, if the need arises, we can further combine the combinations that have the same symmetry. Take a hypothetical molecule AH5 with trigonal bipyramidal structure (D3h symmetry) as an example. Figure 7.1.9 shows a convenient coordinate system for this molecule. It is clear that these are two sets of hydrogen atoms: equatorial hydrogens Hc , Hd , and He and axial hydrogens Ha and Hb . When we linearly combine the orbitals on Ha and Hb , two (un-normalized) combinations are obtained: 1sa + 1sb (A,1 symmetry), 1sa − 1sb (A,,2 ). On the other hand, the combinations for the orbitals on the equatorial hydrogens are 1sc + 1sd + 1se (A,1 ); 2(1sc ) − 1sd − 1se and 1sd − 1se (E , symmetry). If we assume central atom A contributes ns and np orbitals to bonding, we can easily arrive at the results summarized in Table 7.1.4. Note that we can further combine the two ligand linear combinations with A,1 symmetry by taking their sum and difference. Finally, we treat the highly symmetrical octahedral molecule AH6 with Oh symmetry. A coordinate system for this molecule is shown in Fig. 7.1.10. If we assume that central atom A contributes ns, np, and nd orbitals to bonding, the

Application of Group Theory to Molecular Systems

221

Table 7.1.5. Formation of the molecular orbitals in AH6

Symmetry Orbital on A

Orbitals on H

A1g

ns

Eg

D

(6)−1/2 (1sa + 1sb + 1sc + 1sd + 1se + 1sf )  −1/2 [(2(1s ) + 2(1s ) − 1s − 1s  (12) e a f b −1sc − 1sd )  1 2 (1sa + 1sb − 1sc − 1sd ) — — —  −1/2 (1s − 1s ) a  (2) b (2)−1/2 (1sc − 1sd )  (2)−1/2 (1se − 1sf )

ndz2 ndx2 −y2

  ndxy ndyz  nd  xz  npx npy  npz

T2g

T1u

Molecular Orbitals 1a1 , 2a1 1eg , 2eg

1t2g

1t1u , 2t1u

secular determinant has the dimensions 15×15. To obtain the symmetries of the six 1s orbital linear combinations: Oh ΓH

E 6

8C 3 0

6C 2 0

6C 4 2

3C 2 = C24 2

i 0

6S 4 0

8S 6 0

3σ h 4

6σ d 2

≡ A1g + Eg + T1u

To derive the combinations, we need the following tabulation listing the effect of various symmetry operations of Oh on the 1s orbital on hydrogen atom Ha : Oh 1sa

E 8C 3 1sa 2(1sc ), 2(1sd ), 2(1se ), 2(1sf )

6C 2 2(1sb ), 1sc ,1sd , 1se ,1sf

6C 4 2(1sa ), 1sc ,1sd , 1se ,1sf

3C 2 = C24 1sa , 2(1sb )

i 1sb

6S 4 2(1sb ), 1sc ,1sd , 1se ,1sf

8S 6 2(1sc ), 2(1sd ), 2(1se ), 2(1sf )

3σ h 2(1sa ), 1 sb

6σ d 2(1sa ), 1sc ,1sd , 1se ,1sf

Now it is straightforward to derive the results summarized in Table 7.1.5. It is clear that the 15×15 secular determinant is block-factored into three 1×1 determinants that form a T2g set, one 2×2 with A1g symmetry, two 2×2 that form an Eg set, and three 2×2 that form a T1u set. In other words, we only need to solve one 1×1 and three 2×2 secular determinants for this highly symmetrical molecule. This example shows the great simplification that group theory brings to the solution of a large secular determinant.

C2' (σv) a f

7.1.2

b

Hückel theory for cyclic conjugated polyenes

Previously in Chapter 3 we introduced the Hückel molecular orbital theory and applied it to the π system of a number of conjugated polyene chains. In this section we will apply this approximation to cyclic conjugated polyenes, taking advantage of the symmetry properties of these systems in the process. Now let us take benzene as an example. The six 2p atomic orbitals taking part in the π bonding are labeled in the manner shown in Fig. 7.1.11. In the

C2'' (σd) e

c d

Fig. 7.1.11.

Labeling of the 2p orbitals taking part in the π bonding of benzene. Also shown are the locations of the symmetry elements C2, , C2,, , σv and σd .

222

Symmetry in Chemistry Hückel approximation, the 6×6 secular determinant has the form , , α−E , , β , , 0 , , 0 , , 0 , , β

0 β α−E β 0 0

β α−E β 0 0 0

0 0 β α−E β 0

0 0 0 β α−E β

, , , , , , , = 0. , , , , ,

β 0 0 0 β α−E

(7.1.21)

If we consider the D6h symmetry of the system, we can determine the symmetries of the six π molecular orbitals: D6h

E

2C 6

2C 3

C2

3C ,2

3C ,,2

i

Γπ

6

0

0

0

-2

0

0 0

2S 3

2S 6

σh

3σ d

3σ v

0

−6

0

2

≡ A2u + B2g + E1g + E2u

Recall that the character of an operation is equal to the number of vectors unshifted by that operation. Previously, for AHn molecules, in determining ΓH , the 1s orbitals on the hydrogen atoms are spherically symmetric. In the present case, however, the 2p orbitals have directional properties. Take σh as an example. Upon reflection, the direction of the 2p orbitals is reversed. Hence χ (σ h ) = −6. Upon decomposing Γπ , we can conclude that the secular determinant in eq. (7.1.21) can be factored into six 1×1 blocks: one with A2u symmetry, one with B2g symmetry, two others composing an E1g set (with the same root), and the remaining two forming an E2u set (also with the same root). To derive the six linear combinations, we make use of the following results: D6h

E

2C 6

2C 3

C2

3C ,2

3C ,, 2

pa

pa

pb , pf

pc , pe

pd

−pa , −pc ,

−pb , −pd ,

−pe

−pf

i

2S 3

2S 6

σh

−pd

−pc , −pe

−pb , −pf

−pa

3σ d

3σ v

pb , pd , pf

pa , pc , pe

The derivation of the non-degenerate linear combinations are straightforward: P A2u (pa ) = (6)−1/2 (pa + pb + pc + pd + pe + pf )

(after normalization). (7.1.22)

P B2g (pa ) = (6)−1/2 (pa − pb + pc − pd + pe − pf )

(after normalization). (7.1.23)

The first component of the E1g set can also be derived easily: P E1g (pa ) = (12)−1/2 [2(pa ) + pb − pc − 2(pd ) − pe + pf ] (after normalization).

(7.1.24)

For the second component, we operate P E1g on pb an pc : P E1g (pb ) = pa + 2(pb ) + pc − pd − 2(pe ) − pf ,

P E1g (pc ) = −pa + pb + 2(pc ) + pd − pe − 2(pf ).

(7.1.25) (7.1.26)

Application of Group Theory to Molecular Systems

223

Since subtracting eq. (7.1.26) from eq. (7.1.25) yields eq. (7.1.24) (aside from a normalization constant), we need to take the sum of these two equations: Eq. (7.1.25) + Eq. (7.1.26) :

1 (pb + pc − pe − pf ) (after normalization). 2 (7.1.27)

Similar manipulation leads to the following two linear combinations forming the E2u set: E2u :

)

(12)−1/2 [2(pa ) − pb − pc + 2(pd ) − pe − pf ], 1 2 (pb − pc + pe − pf )

(7.1.28) (7.1.29)

The energy of the six molecular orbitals can now be calculated, using the Hückel approximation as discussed in Chapter 3: E(a2u ) = α + 2β,

(7.1.30)

E(e2u ) = α − β,

(7.1.32)

E(e1g ) = α + β,

(7.1.31)

E(b2g ) = α − 2β

(7.1.33)

The π energy levels, along with the molecular orbital wavefunctions, are pictorially displayed in Fig. 7.1.12. Since there are six π electrons in benzene, orbitals a2u and e1g are filled, giving rise to a 1 A1g ground state with the total π energy Eπ = 6α + 8β.

(7.1.34)

–

α− 2β

b2g –

α−β

e2u

–

+

+

+

+

– +

–

–

–

+

–

+

–

+

–

+

–

+

E

α+β

+

e1g

+

–

– –

α +2 β

a2u

+ +

+

+

+ +

Fig. 7.1.12.

The energy level diagram and the wavefunctions of the six π molecular orbitals in benzene.

224

Symmetry in Chemistry If the three π bonds in benzene were independent of each other, i.e., localized, they would have energy 3(2α + 2β) = 6α + 6β. Hence the delocalization energy (DE) for benzene is DE = 6α + 8β − 6α − 6β = 2β.

(7.1.35)

Calculation of β from first principles is a fairly complicated task. On the other hand, it can be approximated from experimental data: |β| ∼ 18 kcal mol−1 = 75 kJ mol−1 .

x

h g

i

a b

y f

(7.1.36)

Another example of a cyclic conjugated polyene system is naphthalene. A coordinate system for this molecule, along with the labeling of the π atomic orbitals, is shown in Fig. 7.1.13. The 10×10 secular determinant has the form:

c e

j

d

Fig. 7.1.13.

Labelling of the 2p orbitals taking part in the π bonding of naphthalene. The z axis points outward.

, , α−E , , β , , 0 , , 0 , , 0 , , , 0 , , 0 , , 0 , , β , , 0

β α−E β 0 0 0 0 0 0 0

0 β α−E β 0 0 0 0 0 0

0 0 β α−E 0 0 0 0 0 β

0 0 0 0 α−E β 0 0 0 β

0 0 0 0 β α−E β 0 0 0

0 0 0 0 0 β α−E β 0 0

0 0 0 0 0 0 β α−E β 0

β 0 0 0 0 0 0 β α−E β

0 0 0 β β 0 0 0 β α−E

, , , , , , , , , , , , = 0. , , , , , , , , ,

(7.1.37)

With the aid of the D2h character table, we can determine the symmetries of the ten molecular orbitals of this system: D2h Γπ

E 10

C 2 (z) 0

C 2 (y) 0

C 2 (x) −2

i 0

σ (xy) −10

σ (xz) 2

σ (yz) 0

≡ 2Au + 3B2g + 2B3g + 3B1u

In other words, the secular determinant in eq. (7.1.37) can be factored into two 2×2 and two 3×3 blocks. To obtain the explicit forms of these ten combinations, we need the results of each of the eight symmetry operations. Also, since the system now has three types of (structurally non-equivalent) carbon atoms, we need the operation results on the 2p orbitals of these three kinds of atoms: D2h pa pb pi

E pa pb pi

C 2 (z) C 2 (y) pe −pd pf −pc pj −pj

C 2 (x) i −ph −pe −pg −pf −pi −pj

σ (xy) −pa −pb −pi

σ (xz) ph pg pi

σ (yz) pd pc pj

The resultant combinations can be obtained easily: 1 (pa − pd + pe − ph ), 2 1 φ2 = (pb − pc + pf − pg ); 2

Au : φ1 =

(7.1.38) (7.1.39)

Application of Group Theory to Molecular Systems 1 (pa − pd − pe + ph ), 2 1 φ4 = (pb − pc − pf + pg ), 2

B2g : φ3 =

φ5 = (2)−1/2 (pi − pj );

1 (pa + pd − pe − ph ), 2 1 φ7 = (pb + pc − pf − pg ); 2 1 B1u : φ8 = (pa + pd + pe + ph ), 2 1 φ9 = (pb + pc + pf + pg ), 2 B3g : φ6 =

φ10 = (2)−1/2 (pi + pj ).

(7.1.40) (7.1.41) (7.1.42) (7.1.43) (7.1.44) (7.1.45) (7.1.46) (7.1.47)

Next we need to set up the four smaller secular determinants. Take the one with Au symmetry as an example: H11 = ∫ φ1 Hˆ φ1 dτ ' 1 = (pa − pd + pe − ph )Hˆ (pa − pd + pe − ph )dτ = α; 4

H12 = ∫ φ1 Hˆ φ2 dτ ' 1 = (pa − pd + pe − ph )Hˆ (pb − pc + pf − pg )dτ = β; 4

(7.1.48)

(7.1.49)

H22 = ∫ φ2 Hˆ φ2 dτ ' 1 = (pb − pc + pf − pg )Hˆ (pb − pc + pf − pg )dτ = α − β. 4 (7.1.50) Thus the Au secular determinant has the form , , α−E β Au : ,, β α−β −E

, , , = 0. ,

The other three determinants can be obtained in a similar manner: , , , α−E β (2)1/2 β ,, , , , β α−β −E 0 B2g : , , = 0. , , , (2)1/2 β 0 α−β −E , , , , α−E , β , , = 0. B3g : , β α+β −E , , , , α−E β (2)1/2 β ,, , , , β α+β −E 0 B1u : , , = 0. , , , (2)1/2 β 0 α+β −E ,

(7.1.51)

(7.1.52)

(7.1.53)

(7.1.54)

225

226

Symmetry in Chemistry Table 7.1.6. The Hückel energies and wavefunctions of the π molecular orbitals in

naphthalene

↑ E

Orbital

Energy

Wavefunction

3b2g 2au 3b1u 2b2g 2b3g 1au 2b1u 1b2g 1b3g 1b1u

α − 2.303β α – 1.618β α – 1.303β α−β α – 0.618β α + 0.618β α+β α + 1.303β α + 1.618β α + 2.303β

0.3006(pa − pd − pe + ph ) − 0.2307(pb − pc − pf 0.2629(pa − pd + pe − ph ) − 0.4253(pb − pc + pf 0.3996(pa + pd + pe + ph ) − 0.1735(pb + pc + pf 0.4082(pb − pc − pf + pg ) − 0.4082(pi − pj ) 0.4253(pa + pd − pe − ph ) − 0.2629(pb + pc − pf 0.4253(pa − pd + pe − ph ) + 0.2629(pb − pc + pf 0.4082(pb + pc + pf + pg ) − 0.4082(pi − pj ) 0.3996(pa − pd − pe + ph ) + 0.1735(pb − pc − pf 0.2629(pa + pd − pe − ph ) + 0.4253(pb + pc − pf 0.3006(pa + pd + pe + ph ) + 0.2307(pb + pc + pf

+ pg ) − 0.4614(pi − pj ) − pg ) + pg ) − 0.3470(pi + pj ) − pg ) − pg ) + pg ) + 0.3470(pi − pj ) − pg ) + pg ) + 0.4614(pi + pj )

The solving of these determinants may be facilitated by the substitution x = (α − E)/β. In any event, the energies of the ten molecular orbitals can be obtained readily. With the energies we can then solve the corresponding secular equations for the coefficients. The energies and the wavefunctions of the ten π molecular orbitals for naphthalene are summarized in Table 7.1.6. From these results, we can arrive at the following ground electronic configuration and state: (1b1u )2 (1b3g )2 (1b2g )2 (2b1u )2 (1au )2 , 1Ag . By adding up the energies for all ten π electrons, we get Eπ = 10α + 13.684β,

(7.1.55)

DE = 3.684β.

(7.1.56)

and

In addition, we can obtain the following allowed electronic transitions: 1 1 1

Ag → [. . . (1au )1 (2b3g )1 ], 1 B3u , Ag → [. . . (1au )1 (2b2g )1 ], 1 B2u ,

x-polarized; y-polarized;

Ag → [. . . (2b1u )1 (1au )2 (2b3g )1 ], 1 B2u ,

y-polarized.

Note that all three transitions are g ↔ u, in accordance with Laporte’s rule. In the previous section, we discussed the construction of the σ molecular orbitals in AHn systems. In this section, we confine our treatment to the π molecular orbitals in cyclic conjugated polyenes. In most molecules, there are σ bonds as well as π bonds, and these systems can be treated by the methods introduced in these two sections. Before concluding this section, it is noted that a fairly user-friendly SHMO (simple Hückel molecular orbital) calculator is now available on the Internet, http://www.chem.ucalgary.ca/shmo/. With this calculator, the Hückel energies and wavefunctions of planar conjugated molecules can be obtained “on the fly.”

Application of Group Theory to Molecular Systems

227

Table 7.1.7. Some useful steps in the derivation of the linear combinations of atomic

orbitals for the π system of (NPX2 )3 . D3h

E

2C 3

3C 2

σh

2S 3

3σ v

Γp Γd c d

3 3 c d

0 0 −a, −e −b, −f

−1 1 a, −c, e −b, d , −f

−3 −3 −c −d

0 0 a, e b, f

1 −1 −a, c, −e b, −d , f

7.1.3

≡ A,,2 + E ,, ≡ A,,1 + E ,,

Cyclic systems involving d orbitals

Sometimes a cyclic π system also involves d orbitals. An example of such a system is the inorganic phosphonitrilic halide (NPX2 )3 , which has D3h symmetry with a pair of out-of-plane halide groups σ -bonded to each phosphorous atom. Now the six atomic orbitals taking part in the π bonding are the three p orbitals on nitrogen and the three d orbitals on phosphorus. These orbitals and their signed lobes above the molecular plane are shown in Fig. 7.1.14. Note that the overlap of the six orbitals is not as efficient as that found in benzene. There is an inevitable “mismatch” of symmetry, here occurring between orbitals a and f , among the six atomic orbitals. The incorporation of the d orbitals complicates the group theoretic procedure to some extent. Table 7.1.7 gives some useful steps in the derivation of the linear combinations of six atomic orbitals. With the results in Table 7.1.7, the linear combination of the atomic orbitals can be readily derived: ,,

P A2 c ⇒ (3)−1/2 (a − c + e)

For the degenerate

E ,,

(after normalization).

(7.1.57)

pair, we have ,,

P E a = 2a + c − e ,,

P E c = a + 2c + e ,,

P E e = −a + c + 2e. Since the first expression is the difference of the last two expressions, we can select the first expression as well as the sum of the last two: ,,

E :

)

(6)−1/2 (2a + c − e) . (2)−1/2 (c + e)

(7.1.58)

Similarly, for the phosphorus 3d orbitals, we have: ,,

P A1 b ⇒ (3)−1/2 (b − d + f ) (after normalization). ) (6)−1/2 (b + 2d + f ) E ,, : . (2)−1/2 (b − f )

(7.1.59) (7.1.60)

It is not difficult to show that, when we form the 2×2 secular determinants with E ,, symmetry, the first component of (7.1.58) interacts with the second component of (7.1.60). Analogously, the second component of (7.1.58) interacts

+ N Pf

+

N +

+

a

b

e

d

c

P N

P +

Fig. 7.1.14.

Labeling of the N 2p orbitals and P 3d orbitals taking part in the π bonding of (NPX2 )3 . Note that only the signed lobes above the molecular plane are shown. Also, a “mismatch,” in this case occurring between orbitals a and f , is inevitable.

228

Symmetry in Chemistry -k'(2 a + c - e ) + ( b - f )

2a + c - e + k( b - f ) + N

+ Pf N

a b

e d

+

+

c

P

P

a-c+e

N

c + e + k( b + 2 d + f )

+

+

P

P

N

N

+

b-d+f

+ N

P

N

N

P

N

N

+

P

N P

+

N

P

+

P

P

N

N

+

N +

-k'( c + e ) + ( b + 2d + f ) +

P

+

N

P +

+

P

P

N P

P

+

N +

+

+

1a 1 ''

1a 2 ''

1e ''

2e ''

E Fig. 7.1.15.

The six pi molecular orbitals of (NPX2 )3 .

with the first component of (7.1.60). Without further quantitative treatment, it is apparent that the six πgolecular orbitals have the energy ordering and nodal characters shown in Fig. 7.1.15. Molecular orbitals 1e,, and 2e,, may be classified as bonding and antibonding, respectively, while 1a2,, and 1a1,, may be considered as nonbonding orbitals. The ground configuration for this system is (1e,, )4 (1a2,, )2 . It is clear that the delocalization of the six π electrons of this compound is not as extensive as that in benzene. As a result, the P3 N3 cycle is not as rigid as the benzene ring. Furthermore, it should be noted that the phosphorus d oribital participation in the bonding of this type of compounds has played an important role in the development of inorganic chemistry. Indeed, the phosphorus d orbitals can participate in the bonding of the (NPX2 )3 molecule in a variety of ways, as discussed in Chapter 15. The presentation here is mainly concerned with the symmetry properties of the π molecular orbitals. 7.1.4

Linear combinations of ligand orbitals for AL4 molecules with Td symmetry

In previous discussion, we constructed the symmetry-adapted linear combinations of the hydrogen 1s orbitals for AHn molecules. In this section, we consider ALn molecules, where L is a ligand capable of both σ and π bonding. For such systems, the procedure to derive the linear combinations of ligand orbitals can become fairly complicated. As an illustration, we take an AL4 molecule with Td symmetry as an example.

Application of Group Theory to Molecular Systems

229

Z

z4

y4

x4

L4

z1

x1 L1

y1 A

x2

X

x3

Y

L2

y3

y2 z2

L3

Fig. 7.1.16.

Coordinate system for a tetrahedral AL4 molecule.

z3

The coordinate systems for all five atoms in AL4 are shown in Fig. 7.1.16. Note that all of them are right-handed. Also, x1 and x4 lie in the AL1 L4 plane, while x2 and x3 lie in the AL2 L3 plane. The four linear combinations with A1 and T2 symmetries of the four vectors z1 , . . . , z4 forming σ bonds with orbitals on atom A may be easily obtained by the technique of projection operators. Therefore, only the results are given in Table 7.1.8, where all linear combinations of ligand orbitals will be listed. It is noted that the four combinations of the z1 vectors are identical to the combinations of hydrogen 1s orbitals obtained for methane. The remaining eight vectors, x1 , . . ., x4 and y1 , . . ., y4 , will form eight linear combinations having symmetries E, T1 , and T2 . In order to see how these ligand vectors transform under the 24 symmetry operations of the Td point group, the direction numbers of all the ligand vectors are required. They are x1 (−1, −1, 2) x2 (−1, 1, 2) y2 (1, 1, 0) y1 (1, −1, 0) z2 (−1, 1, −1) z1 (1, 1, 1)

x3 (1, −1, 2) x4 (1, 1, 2) y3 (−1, −1, 0) y4 (−1, 1, 0) z3 (1, −1, −1) z4 (−1, −1, 1).

Among these, the direction numbers of the four z vectors are obvious. From these four vectors, any other vector may be generated by doing the cross product between an appropriate pair of vectors. For instance, y1 = z1 × z4 , x1 = y1 × z1 , etc. Next we write down the transformation matrices for all the operations: C 3 (i): A threefold axis passing through atoms A and Li , , 0 , , C 3 (1) = ,, 1 , , 0

0 0 1

, , , 0 1 ,, , , , , 0 , C 3 (2) = ,, −1 , , , 0 0 ,

0 0 −1

, , , 0 1 ,, , , , , 0 , C 3 (3) = ,, −1 , , , 0 0 ,

0 0 1

, , , 0 −1 ,, , , , , 0 , C 3 (4) = ,, 1 , , , 0 0 ,

0 0 −1

, −1 ,, , 0 ,, . , 0 ,

2 Note that the matrix for C −1 3 (i), or C 3 (i), is simply the transpose of C 3 (i). C 2 (q): A twofold axis which coincides with axis q on atom A

, , 1 , , C 2 (X ) = , 0 , , 0

0 −1 0

, , , , 0 , , −1 , 0

, , −1 , , C 2 (Y ) = , 0 , , 0

0 1 0

, , , , 0 , , −1 , 0

, , −1 , , C 2 (Z) = , 0 , , 0

0 −1 0

, 0 ,, , 0 ,. , 1 ,

230

Symmetry in Chemistry S 4 (q): Again, the axis of this operation coincides with axis q on atom A , , −1 , , S 4 (X ) = , 0 , , 0

0 0 1

0 −1 0

, , , , , , ,

, , 0 , , S 4 (Y ) = , 0 , , −1

0 −1 0

1 0 0

, , , , , , ,

, , 0 , , S 4 (Z) = , 1 , , 0

−1 0 0

0 0 1

, , , , ,. , ,

3 Note that the matrix for S −1 4 (q), or S 4 (q), is also simply the transpose of S 4 (q). σ (ij): A symmetry plane passing through atoms A, Li , and Lj , , , , , , , 0 0 1 , , 1 0 0 , , 0 1 0 , , , , , , , σ (12) = ,, 0 1 0 ,, σ (13) = ,, 0 0 1 ,, σ (14) = ,, 1 0 0 ,, . , 1 0 0 , , 0 1 0 , , 0 0 1 ,

, , 0 , σ (23) = ,, −1 , 0

−1 0 0

0 0 1

, , , , 1 , , , σ (24) = , 0 , , , , 0

0 0 −1

0 −1 0

, , , , 0 , , , σ (34) = , 0 , , , , −1

0 1 0

−1 0 0

, , , ,. , ,

So now we have the transformation matrices of all the symmetry operations in the Td point group, except the identity operation E, which is simply a unit matrix with the dimensions 3 × 3. When we carry out mathematically a symmetry operation on a ligand vector, we perform a matrix multiplication between the symmetry operation matrix and the vector composed of its directional numbers. For instance, when we operate C 3 (1) on x1 , we do the following: , ,, , , , , 0 0 1 , , −1 , , 2 , , ,, , , , C 3 (1)x1 = ,, 1 0 0 ,, ,, −1 ,, = ,, −1 ,, . , 0 1 0 , , 2 , , −1 , Since operation C 3 (1) does not change the position of ligand L1 , the above resultant new vector (2, −1, −1) may be resolved along the x1 and y1 directions by taking the dot products 1 (6)−1/2 (2, −1, −1) · (6)−1/2 (−1, −1, 2) = − x1 2 1 (6)−1/2 (2, −1, −1) · (2)−1/2 (1, −1, 0) = (3)1/2 y1 . 2

1 1 In other words, C 3 (1)x1 = − x1 + (3)1/2 y1 . Note that when we resolve 2 2 the new vector along the x1 and y1 directions, all vectors involved need to be normalized first. Similarly, when we operate C 3 (2) on x1 , we get C 3 (2)x1 = (2, 1, 1). Since operation C 3 (2) on ligand L1 yields L3 , the resultant vector (2, 1, 1) is to be resolved along the x3 and y3 directions. Now it is easy to show C 3 (2)x1 = 1 1 x3 − (3)1/2 y3 . 2 2 When we carry out all 24 symmetry operations in the Td point group on vector x1 , we get 1 1 1 1 C 3 (1) : − x1 + (3)1/2 y1 , C −1 (1) : − x1 − (3)1/2 y1 3 2 2 2 2 1 1 1/2 1 1 1/2 C 3 (2) : x3 − (3) y3 , C −1 y4 3 (2) : − 2 x4 − 2 (3) 2 2

Application of Group Theory to Molecular Systems 1 1 1 1 1/2 C 3 (3) : − x4 + (3)1/2 y4 , C −1 y2 3 (3) : 2 x2 + 2 (3) 2 2 1 1 1 1 C 3 (4) : x2 − (3)1/2 y2 , C −1 (4) : x3 + (3)1/2 y3 . 3 2 2 2 2 After summing up, 8C 3 x1 = −x1 + x2 + x3 − x4 . C 2 (X ) : − x3 ,

C 2 (Y ) : − x2 ,

C 2 (Z) : x4 .

After summing up, 3C 2 x1 = −x2 − x3 + x4 . 1 1 1 1 S 4 (X ) : − x4 − (3)1/2 y4 , S −1 (X ) : x2 + (3)1/2 y2 4 2 2 2 2 1 1 1/2 1 1 1/2 y4 S 4 (Y ) : x3 − (3) y3 , S −1 4 (Y ) : − 2 x4 + 2 (3) 2 2 S 4 (Z) : − x2 ,

S −1 4 (Z) : − x3 .

1 1 1 1 After summing up, 6S 4 x1 = − x2 − x3 − x4 + (3)1/2 y2 − (3)1/2 y3 . 2 2 2 2 1 1 1 1 σ (12) : − x1 + (3)1/2 y1 , σ (13) : − x1 − (3)1/2 y1 , σ (14) : x1 2 2 2 2 1 1 1/2 1 1 σ (23) : x4 , σ (24) : x3 + (3) y3 , σ (34) : x2 − (3)1/2 y2 . 2 2 2 2 1 1 1 1 x2 + x3 + x4 − (3)1/2 y2 + (3)1/2 y3 . 2 2 2 2 Finally, for the identity operation E, we have E, Ex1 = x1 . If we carry out the same 24 symmetry operations on vector y1 , we get

After summing up, 6σ d x1 =

Ey1 = y1 .

8C 3 y1 = −y1 + y2 + y3 − y4 . 3C 2 y1 = −y2 − y3 + y4 .

1 1 1 1 y2 + y3 + y4 + (3)1/2 x2 − (3)1/2 x3 . 2 2 2 2 1 1 1 1/2 1 6σ d y1 = − y2 − y3 − y4 − (3) x2 + (3)1/2 x3 . 2 2 2 2

6S 4 y1 =

Now we are in a position to apply the projection operator to obtain the linear combinations of ligand orbitals with the desired symmetry. For instance, for the two linear combinations that form the degenerate set with E symmetry, we carry out the operations P E x1 = 3x1 − 3x2 − 3x3 + 3x4 ,

or

1 (x1 − x2 − x3 + x4 ). 2

1 (y1 −y2 −y3 +y4 ). All linear combinations may be obtained 2 in an analogous manner. Table 7.1.8 lists the 16 linear combinations of ligand orbitals for an AL4 molecule with Td symmetry. Similarly, P E y1 =

231

232

Symmetry in Chemistry Table 7.1.8. The symmetry-adapted linear combinations of ligand orbitals for an AL4 molecule

with Td symmetry

Symmetry Orbital on A Orbitals on ligands A1 E

s D

dz 2

dx2 −y2

1 (s + s + s + s ); 1 (z + z + z + z ) 2 3 4 2 3 4 2 1 2 1 1 (x − x − x + x ) 2 3 4 2 1 1 (y − y − y + y ) 2 3 4 2 1

D

 1  1    4 [(3) 2 (x1 + x2 − x3 − x4 ) + (y1 + y2 − y3 − y4 )]

T1

T1

Molecular orbitals

      

   px py   pz   d  yz dxz   dxy

          

1 1 [(3) 2 (x − x + x − x ) + (y − y + y − y )] 1 2 3 4 1 2 3 4 4 1 (y + y + y + y ) 2 3 4 2 1  1 (s − s + s − s ) 1  2 3 4  2 (z1 − z2 + z3 − z4 ) 2 1 1 (s + s − s − s ) 1 (z + z − z − z ) 2 3 4 1 2 3 4 2 1   21 1 (s − s − s + s ) 1 2 3 4 2 2 (z1 − z2 − z3 + z4 ) 1 1 [(x + x − x − x ) + (3) 2 (−y − y + y + y )] 1 2 3 4 1 2 3 4 4 1 1 [(x − x + x − x ) + (3) 2 (y − y + y − y )] 1 2 3 4 1 2 3 4 4 1 (x + x + x + x ) 2 3 4 2 1

1a1 , 2a1 , 3a1 1e , 2 e

1t1

1t2 , 2t2 , 3t2 , 4t2 , 5t2

For an AL4 molecule with Td symmetry, if we assume that nine atomic orbitals on A and four atomic orbitals on each L participate in bonding, there will be 25 molecular orbitals in total. Based on symmetry arguments, as shown in Table 7.1.8, among the molecular orbitals formed, there will be three with a1 symmetry, two doubly degenerate sets with E symmetry, one triply degenerate set with T1 symmetry (which is nonbonding, i.e., localized on the ligands), and five triply degenerate set with T2 symmetry. Clearly, for such a complex system, it is not straightforward to come up with a qualitative energy level diagram.

7.2

Construction of hybrid orbitals

As introduced in Chapter 3, for AXn systems, the hybrid orbitals are the linear combinations of atomic orbitals on central atom A that point toward the X atoms. In addition, the construction of the spn hybrids was demonstrated. In this section, we will consider hybrids that have d–orbital contributions, as well as the relationship between the hybrid orbital coefficient matrix and that of the molecular orbitals, all from the viewpoint of group theory. 7.2.1

Hybridization schemes

As is well known, if we construct four equivalent hybrid orbitals using one s and three p atomic orbitals, the hybrids would point toward the four corners of a tetrahedron. However, is this the only way to construct four such hybrids? If not, what other atomic orbitals can be used to form such hybrid orbitals? To answer these questions, we need to determine the representations spanned by the four hybrid orbitals that point toward the corners of a tetrahedron: Td Γσ

E 4

8C 3 1

3C 2 0

6S 4 0

6σ d 2

≡ A1 + T2

Application of Group Theory to Molecular Systems This result implies that, among the four required atomic orbitals (on the central atom), one must have A1 symmetry and the other three must form a T2 set. From Areas III and IV of the Td character table, we know that the s orbital has A1 symmetry, while the three p orbitals, or the dxy , dyz , and dxz orbitals, collectively form a T2 set. In other words, the hybridization scheme can be either the well-known sp3 or the less familiar sd 3 , or a combination of these two schemes. On symmetry grounds, the sp3 and sd 3 schemes are entirely equivalent to each other. However, for a particular molecule, we can readily see that one scheme is favored over the other. For instance, in CH4 , carbon can use the 2s and three 2p orbitals to form a set of sp3 hybrids. It is also clear that carbon is unlikely to use its 2s orbital and three 3d orbitals (which lie above the 2p orbitals by about 950 kJ mol−1 ) to form the hybrids. On the other hand, for tetrahedral transition metal ions such as MnO− 4 , it is likely that Mn would use three 3d orbitals, instead of the three higher energy 4p orbitals, for the formation of the hybrids. We now list the possible hybridization schemes for several important molecular types. (1) AX3 , trigonal planar, D3h symmetry: D3h

E

2C 3

3C 2

σh

2S 3

3σ v

Γσ

3

0

1

3

0

1

≡ A,1 (s; dz2 ) + E,[(px , py ); (dxy , dx2 −y2 )]

Hence the possible schemes include sp2 , sd 2 , dp2 , and d 3 . (2) AX4 , square planar, D4h symmetry: D4h

E

2C 4

C2

2C 2 ,

2C 2 ,,

i

2S 4

σh

2σ v

2σ d

Γσ

4

0

0

2

0

0

0

4

2

0

≡ A1g (s; d 2 ) + B1g (d 2 2 )+Eu (px , py ) z x −y

Hence the possible schemes include dsp2 and d 2 p2 . (3) AX5 , trigonal bipyramidal, D3h symmetry: D3h

E

2C 3

3C 2

σh

2S 3

3σ v

Γσ

5

2

1

3

0

3

≡ 2A,1 (s; dz 2 ) + A,,2 (pz ) + E,[(px , py ); (dxy , dx2 −y2 )]

Hence the possible schemes include dsp3 and d 3 sp. (4) AX6 , octahedral, Oh symmetry: Oh

E

8C 3

6C 2

6C 4

3C 2

i

6S 4

8S 6

3σ h

6σ d

Γσ

6

0

0

2

2

0

0

0

4

2

≡ A1g (s) + Eg (d 2 , d 2 2 )+T1u (px , py , pz ) z x −y

So the only possible scheme is d 2 sp3 . Once we have determined the atomic orbitals taking part in the formation of the hybrids, we can employ the method outlined in Chapter 3 to obtain the explicit expressions of the hybrid orbitals. 7.2.2

Relationship between the coefficient matrices for the hybrid and molecular orbital wavefunctions

As has been mentioned more than once already, to construct the hybrid orbitals for an AXn molecule, we linearly combine the atomic orbitals on A so that the

233

234

Symmetry in Chemistry resultant hybrid orbitals point toward the X ligands. On the other hand, to form the molecular orbitals for the AXn molecule, we linearly combine the orbitals on the ligands such that the combinations match in symmetry with the orbitals on A. Upon studying these two statements, we would not be surprised to find that the coefficient matrices for the hybrid orbitals and for the ligand orbital linear combinations are related to each other. The basis for this relationship is that both matrices are derived by considering the symmetry properties of the molecule. Indeed, this relationship is obvious if we take up a specific example. From eq. (3.4.31), the sp2 hybrids for an AX3 (or AH3 ) molecule with D3h symmetry is: , , , , h1 , , (3)−1/2 , , , , h2 , = , (3)−1/2 , , , , h3 , , (3)−1/2

(2/3)1/2 −(6)−1/2 −(6)−1/2

0

(2)−1/2 −(2)−1/2

,, , ,, s , ,, , , , px , . ,, , , , py ,

(7.2.1)

From Table 7.1.2, the linear combinations of ligand orbitals for BH3 have the form , , (3)−1/2 , , (2/3)1/2 , , 0

(3)−1/2 −(6)−1/2 (2)−1/2

(3)−1/2 −(6)−1/2 −(2)−1/2

,, , , , 1sa , ,, , , , 1sb , . ,, , , , 1sc ,

(7.2.2)

It is now obvious that the matrix in eq. (7.2.1) is simply the transpose of the matrix in expression (7.2.2), and vice versa. In addition, it can be easily checked that the coefficient matrix for the sp3 hybrids given in eq. (3.4.35) and the coefficient matrix for the linear combinations of ligand orbitals in CH4 (Table 7.1.3) have the same relationship. To conclude, there are two ways to determine the explicit expressions of a set of hybrid orbitals. The first one is that outlined in Chapter 3, taking advantage of the orthonormality relationship among the hybrids as well as the geometry and symmetry of the system. The second method is to apply the appropriate projection operators to the ligand orbitals, which are placed at the ends of the hybrids, to obtain the linear combinations of the ligand orbitals. The coefficient matrix for the hybrids is simply the transpose of the coefficient matrix for the linear combinations. These two methods are naturally closely related to one another. The only difference is that the latter formally makes use of group theory techniques, such as projection operator application and decomposition of a reducible representation, whereas the former does not. 7.2.3

Hybrids with d-orbital participation

In Section 7.2.1, we have seen that many hybridization schemes involve d orbitals. In fact, we do not anticipate any technical difficulty in the construction of hybrids that have d orbital participation. Let us take octahedral d 2 sp3 hybrids, directed along Cartesian axes (Fig. 7.1.10), as an example. From Table 7.1.5,

Application of Group Theory to Molecular Systems we have the coefficient matrix for the linear combinations of ligand orbitals: , , (6)−1/2 , , −(12)−1/2 , , 1/2 , , , (2)−1/2 , , 0 , , 0

(6)−1/2 −(12)−1/2 1/2 −(2)−1/2 0 0

(6)−1/2 −(12)−1/2 −1/2 0 (2)−1/2 0

(6)−1/2 −(12)−1/2 −1/2 0 −(2)−1/2 0

(6)−1/2 2(12)−1/2 0 0 0 (2)−1/2

(6)−1/2 2(12)−1/2 0 0 0 −(2)−1/2

,, ,, ,, ,, ,, ,, ,, ,, ,, ,, ,, ,, ,,

1sa 1sb 1sc 1sd 1se 1sf

With these results, we can easily obtain the hybrid wavefunctions , , , , , , , , , ,

ha hb hc hd he hf

, , , , , , , , , , ,=, , , , , , , , ,

(6)−1/2 (6)−1/2 (6)−1/2 (6)−1/2 (6)−1/2 (6)−1/2

−(12)−1/2 −(12)−1/2 −(12)−1/2 −(12)−1/2 2(12)−1/2 2(12)−1/2

1/2 1/2 −1/2 −1/2 0 0

(2)−1/2 −(2)−1/2 0 0 0 0

0 0 (2)−1/2 −(2)−1/2 0 0

0 0 0 0 (2)−1/2 −(2)−1/2

,, ,, ,, ,, ,, ,, ,, ,, ,, ,,

, , , , , , , , , , , , ,

, , , , dx2 −y2 ,, ,. px , py , , pz (7.2.3) s dz2

In eq. (7.2.3), hybrids ha , hb , . . . , hf point toward orbitals 1sa , 1sb , . . . , 1sf , respectively (Fig. 7.1.10). Lastly, we consider a system with non-equivalent positions. An example of such a system is the trigonal bipyramidal molecule AX5 with D3h symmetry. As discussed previously, one possible scheme is the dsp3 hybridization, where dz2 is the only d orbital participating. If we use the dz2 and pz orbitals for the construction of axial hybrids ha and hb , and the s, px , and py orbitals for the equatorial hybrids hc , hd , and he (Fig. 7.1.8), we can readily write down the wavefunctions of these hybrids: , , , , , , , , , ,

ha hb hc hd he

, , , , (2)−1/2 , , , , (2)−1/2 , , ,=, 0 , , , , 0 , , , , 0

(2)−1/2 −(2)−1/2 0 0 0

0 0

(3)−1/2 (3)−1/2 (3)−1/2

0 0 2(6)−1/2 −(6)−1/2 −(6)−1/2

0 0 0

(2)−1/2 −(2)−1/2

,, ,, ,, ,, ,, ,, ,, ,, ,, ,,

, dz2 ,, pz ,, s ,, px ,, py , (7.2.4)

However, there is no reason at all to assume ha and hb are made up of only pz and dz2 orbitals: The dz2 orbital can also contribute to the equatorial hybrids, and the s orbital can also contribute to the axial hybrids. In fact, if we use only the s and pz orbitals for the axial hybrids, and the dz2 , px , and py for the equatorial hybrids, we then have , , , , , , , , , ,

ha hb hc hd he

, , , , 0 , , , , 0 , , , = , −(3)−1/2 , , , , −(3)−1/2 , , , , −(3)−1/2

(2)−1/2 −(2)−1/2 0 0 0

(2)−1/2 (2)−1/2 0 0 0

0 0 2(6)−1/2 −(6)−1/2 −(6)−1/2

0 0 0

(2)−1/2 −(2)−1/2

,, ,, ,, ,, ,, ,, ,, ,, ,, ,,

, dz2 ,, pz ,, s ,, . px ,, py , (7.2.5)

235

236

Symmetry in Chemistry Obviously, both of the matrices in eqs. (7.2.4) and (7.2.5) are limiting cases. A general expression encompassing these two cases is

, , , , , , , , ,

ha hb hc hd he

, ,, (2)−1/2 sin α , , , , , , (2)−1/2 sin α , , , = , −(3)−1/2 cos α , , , , −(3)−1/2 cos α , , −(3)−1/2 cos α

(2)−1/2 −(2)−1/2 0 0 0

(2)−1/2 cos α (2)−1/2 cos α (3)−1/2 sin α (3)−1/2 sin α (3)−1/2 sin α

0 0 2(6)−1/2 −(6)−1/2 (2)−1/2 −(6)−1/2 (2)−1/2

0 0 0

,, ,, ,, ,, ,, ,, ,, ,, ,, ,

, dz2 , , pz , , s ,. , px , py , (7.2.6)

To obtain eqs. (7.2.4) and (7.2.5) from eq. (7.2.6), we only need to set angle α to be 90◦ and 0◦ , respectively. It is not difficult to show that the five hybrids form an orthonormal set of wavefunctions. The parameter α in the coefficient matrix in eq. (7.2.6) may be determined in a number of ways, such as by the maximization of overlap between the hybrids and the ligand orbitals, or by the minimization of the energy of the system. In any event, such procedures are clearly beyond the scope of this chapter (or this book) and we will not deal with them any further.

7.3

Molecular vibrations

Molecular vibrations, as detected in infrared and Raman spectroscopy, provide useful information on the geometric and electronic structures of a molecule. As mentioned earlier, each vibrational wavefunction of a molecule must have the symmetry of an irreducible representation of that molecule’s point group. Hence the vibrational motion of a molecule is another topic that may be fruitfully treated by group theory. 7.3.1

The symmetries and activities of the normal modes

A molecule composed of N atoms has in general 3N degrees of freedom, which include three each for translational and rotational motions, and (3N − 6) for the normal vibrations. During a normal vibration, all atoms execute simple harmonic motion at a characteristic frequency about their equilibrium positions. For a linear molecule, there are only two rotational degrees of freedom, and hence (3N − 5) vibrations. Note that normal vibrations that have the same symmetry and frequency constitute the equivalent components of a degenerate normal mode; hence the number of normal modes is always equal to or less than the number of normal vibrations. In the following discussion, we shall demonstrate how to determine the symmetries and activities of the normal modes of a molecule, using NH3 as an example. Step 1. For a molecule belonging to a certain point group, we first determine the representation Γ (N0 ) whose characters are the number of atoms that are unshifted by the operations in the group. Taking the NH3 molecule as an example, C3v Γ (N0 )

E 4

2C 3 1

3σ v 2

Application of Group Theory to Molecular Systems Step 2. Multiply each character of Γ (N0 ) by the appropriate factor f (R) to obtain Γ3N . Now we show how to determine factor f (R) for operation R. When R is a rotation of angle φ, C φ , we use f (C φ ) = 1 + 2 cos φ.

(7.3.1)

Thus, f (E) = 3; f (C 2 ) = −1; f (C 3 ) = f (C 23 ) = 0; f (C 4 ) = f (C 34 ) = 1; f (C 6 ) = f (C 56 ) = 2; etc. When R is an improper rotation of angle φ, S φ , we have f (S φ ) = −1 + 2 cos φ.

(7.3.2)

Thus, f (S 1 ) = f (σ ) = 1; f (S 2 ) = f (i) = −3; f (S 3 ) = −2; f (S 4 ) = f (S 34 ) = −1; f (S 6 ) = f (S 56 ) = 0; etc. So, for NH3 , C3v f (R) Γ3N = f (R) × Γ (N0 )

E 3 12

2C 3 0 0

3σ v 1 2

Note that the values of f (R) can also be obtained from the characters of the symmetry species Γxyz (representation based on x, y, and z). For point group C3v , Γxyz = Γxy (based on x and y) + Γz (based on z) = E + A2 . Upon decomposing Γ3N using e.g. (6.4.3), we get Γ3N (NH3 ) = 3A1 + A2 + 4E. Step 3. From Γ3N subtract the symmetry species Γtrans (= Γxyz ) for the translation of the molecule as a whole and Γrot (based on Rx , Ry , and Rz ) for the rotational motion to obtain the representation for molecular vibration, Γvib : Γvib = Γ3N − Γtrans − Γrot .

(7.3.3)

For NH3 , we have Γvib (NH3 ) = (3A1 + A2 + 4E) − (A1 + E) − (A2 + E) = 2A1 + 2E.

In other words, among the six normal vibrations of NH3 , two have A1 symmetry, two others form a degenerate E set, and the remaining two form another E set. Step 4. For a vibrational mode to be infrared (IR) active, it must bring about a change in the molecule’s dipole moment. Since the symmetry species of the dipole moment’s components are the same as Γx , Γy , and Γz , a normal mode having the same symmetry as Γx , Γy , or Γz will be infrared active. The argument employed here is very similar to that used in the derivation of the selection rules for electric dipole transitions (Section 7.1.3). So, of the six vibrations of NH3 , all are infrared active, and they comprise four normal modes with distinct fundamental frequencies.

237

238

Symmetry in Chemistry

Fig. 7.3.1.

The vibrational modes of NH3 and observed frequencies. Note that only one component is shown for the E modes.

v1(A1)

v2(A1)

3337 cm–1

~950 cm–1

v3a(E ) 3414 cm–1

v4a(E ) 1627 cm–1

On the other hand, for a vibrational mode to be Raman (R) active, it must bring about a change in the polarizability of the molecule. As the components of the polarizability tensor (based on the quadratic products of the coordinates) have the symmetry of Γx2 , Γy2 , Γz2 , Γxy , Γxz , and Γyz , a normal mode having one of these symmetries will be Raman active. So, for NH3 , we again will observe four fundamentals in its Raman spectrum. In other words, Γvib (NH3 ) = 2A1 (R/IR) + 2E(R/IR). The four observed frequencies and the pictorial representations of the normal modes for NH3 are displayed in Fig. 7.3.1. From this figure, we can see that ν1 and ν3 are stretching modes, while ν2 and ν4 are bending modes. Note that the number of stretching vibrations is equal to the number of bonds. Also, the stretching modes have higher frequencies than the bending ones. Before discussing other examples, we note here that, for a centrosymmetric molecule (one with an inversion center), Γx , Γy , and Γz are “u” (from the German word ungerade, meaning odd) species, while binary products of x, y, and z have “g” (gerade, meaning even) symmetry. Thus infrared active modes will be Raman forbidden, and Raman active modes will be infrared forbidden. In other words, there are no coincident infrared and Raman bands for a centrosymmetric molecule. This relationship is known as the rule of mutual exclusion. Another useful relationship: As the totally symmetric irreducible representation ΓTS in every group is always associated with one or more binary products of x, y, and z and it follows that totally symmetric vibrational modes are always Raman active. Besides being always Raman active, the totally symmetric vibrational modes can also be readily identified in the spectrum. As shown in Fig. 7.3.2, the scattered Raman radiation can be resolved into two intensity components, I⊥ and I6 . The ratio of these two intensities is called the depolarization ratio ρ: ρ = I⊥ /I6 .

(7.3.4)

If the incident radiation is plane-polarized, such as that produced by lasers in Raman spectroscopy, scattering theory predicts that totally symmetric modes

Application of Group Theory to Molecular Systems

239

7.3.2

Intensity

will have 0 < ρ < 3/4 and all other (non-totally symmetric) modes will have ρ = 3/4. A vibrational band with 0 < ρ < 3/4 is said to be polarized, and one with ρ = 3/4 is said to be depolarized. In fact, for highly symmetric molecules, the polarized bands often have ρ ∼ 0, which makes identifying totally symmetric modes relatively simple. For the NH3 molecule, the two A1 modes are polarized. Figure 7.3.2 shows the intensities I⊥ and I6 for the ν1 (A1 ) and ν2 (E) Raman bands of CCl4 . It is seen that I⊥ of ν1 (A1 ) is essentially zero. Precise measurements yield ρ = 0.005 ± 0.002 for ν1 (A1 ) and ρ = 0.72 ± 0.002 for ν2 (E). These results are consistent with scattering theory.

Some illustrative examples

In this section, we will attempt to illustrate the various principles and techniques introduced in the previous section with several simple examples. Special emphasis will be on the stretching modes of a molecule.

I ||

I

460 I ||

I

214

(1) trans-N2 F2 The molecule N2 F2 can exist in two geometrical forms, namely, cis and trans. Here we are only concerned with the trans isomer with C2h symmetry. The methodical derivation of the symmetry species of the vibrational modes is best conducted in tabular form, as shown below. C2h

E

C2

Γ (N0 ) 4 0 12 0 Γ3N Γtrans = f (R) 3 −1 Γrot 3 −1 6 2 Γvib

i

σh

0 4 0 4 −3 1 3 −1 0 4

Remark row 1 (atoms not moved by R) row 2 = row 1× row 3 row 3, Γtrans based on (x, y, z) row 4, Γrot based on (Rx , Ry , Rz ) row 5 = row 2 − row 3 − row 4

Hence Γ3N (N2 F2 ) = 4Ag + 2Bg + 2Au + 4Bu , and Γvib (N2 F2 ) = 3Ag (R) + Au (IR) + 2Bu (IR). So trans-N2 F2 has three bands in both its infrared spectrum and its Raman spectrum. However, none of the bands are coincident, as this is a centrosymmetric molecule. The normal modes, as well as their observed frequencies, of trans-N2 F2 are shown in Fig. 7.3.3. Note that this molecule has three bonds and hence has three stretching modes: ν1 (Ag ) is the symmetric stretch of two N–F bonds, ν2 (Ag ) is the N=N stretching, while ν4 (Bu ) is the asymmetric stretch of the two N–F bonds. As the symmetric N–F stretch and N=N stretch have the same symmetry (Ag ), ν1 and ν2 are both mixtures of these two types of stretch motion. Among the three modes, ν2 (Ag ) has the highest energy, as N=N is a double bond and N–F is a single bond.

~ v/cm–1

Fig. 7.3.2.

Raman band intensities I⊥ and I6 of CCl4 for ν1 (A1 ) (top) and ν2 (E) (bottom). The splitting in the ν1 band is due to the isotopic effect of Cl.

240

Symmetry in Chemistry

v1(Ag) (R,pol) 1010 cm–1

v2(Ag) (R,pol) 1522 cm–1

v3(Ag) (R,pol) 600 cm–1 –

Fig. 7.3.3.

+

The vibrational modes and the corresponding frequencies of trans-N2 F2 . Note that only ν1 , ν2 , and ν4 are stretching modes.

+

– v4(Bu) (IR) 990 cm–1

v5(Bu) (IR) 423 cm–1

v6(Au) (IR) 364 cm–1

Fig. 7.3.4.

The vibrational modes and their frequencies of CF4 . Note that only one component is shown for the degenerate modes.

v1(A1) (R) 908 cm–1

v2(E) (R) 435 cm–1

v3(T2) (IR/R) 1283 cm–1

v4(T2) (IR/R) 631 cm–1

(2) CF4 This is a tetrahedral molecule with Td symmetry. The derivation of the vibrational modes is summarized below. Td Γ (N0 ) f (R) Γ3N

E 8C 3 5 2 3 0 15 0

3C 2 1 −1 −1

6S 4 1 −1 −1

6σ d 3 1 3

≡ A1 + E + T1 + 3T2

Γvib (CF4 ) = A1 (R) + E(R) + 2T2 (IR/R)

So CF4 has two infrared bands and four Raman bands, and there are two coincident absorptions. The normal modes and their respective frequencies are given in Fig. 7.3.4. Note that ν1 (A1 ) and ν3 (T2 ) are the stretching bands. Also, this is an example that illustrates the “rule” that a highly symmetrical molecule has very few infrared active vibrations. The basis of the “rule” is that, in a point group with very high symmetry, x, y, and z often combine to form degenerate representations. (3) P4 The atoms in the P4 molecule occupy the corners of a regular tetrahedron. In point group Td , following the previous procedure, we have Td Γ (N0 ) f (R) Γ3N

E 8C 3 4 1 3 0 12 0

3C 2 0 −1 0

6S 4 0 −1 0

6σ d 2 1 2

Γvib (P4 , Td ) = A1 (R) + E(R) + T2 (IR, R).

≡ A1 + E + T1 + 2T2

Application of Group Theory to Molecular Systems

241

Fig. 7.3.5.

ν1(A1), 606 cm

_1

ν2(E), 363 cm

_1

ν3(T2), 465 cm

_1

If the molecule were to adopt a hypothetical square-planar structure in point group D4h , the normal modes would be Γvib (P4 , D4h ) = A1g (R) + B1g (R) + B2g (R) + B2u + Eu (IR). Both models have the same numbers of infrared, Raman, and polarized Raman bands. However, they can be distinguished by the fact that the T2 mode in the Td structure is both IR and Raman active (there is one coincidence), whereas the rule of mutual exclusion holds for the centrosymmetric D4h structure. The normal modes of P4 and their observed Raman frequencies are shown in Fig. 7.3.5. Here A1 is called the breathing mode, since all P–P bonds are stretching and contracting in unison. In the ν2 (E) mode, two bonds are contracting while the other four are lengthening; in the ν3 (T2 ) mode, three bonds are contracting while the other three are lengthening. It is of interest to note that all six vibrations of P4 are stretching motions. (4) XeF4 This molecule has a square-planar structure with D4h symmetry. With reference to the coordinate system displayed in Fig. 7.3.6, the symmetry of the vibrational modes may be derived in the following manner: D4h Γ (N0 ) f (R) Γ3N

E

2C 4

C2

2C ,2

2C ,,2

i

2S 4

σh

2σ v

2σ d

5 3 15

1 1 1

1 −1 −1

3 −1 −3

1 −1 −1

1 −3 −3

1 −1 −1

5 1 5

3 1 3

1 1 1

Γ3N (XeF4 ) = A1g + A2g + B1g + B2g + Eg + 2A2u + B2u + 3Eu .

Γvib (XeF4 ) = A1g (R) + B1g (R) + B2g (R) + A2u (IR) + B2u + 2Eu (IR). (7.3.5)

So XeF4 has three bands in its infrared spectrum as well as in its Raman spectrum. None of the bands are coincident, as this molecule is centrosymmetric. In addition, there is a “silent” mode, with B2u symmetry, which does not show up in either spectrum. The normal modes and their frequencies are given in Fig. 7.3.6.

The normal modes and Raman frequencies of P4 . Only one component is shown for the degenerate modes.

242

Symmetry in Chemistry + b

c

a

d

v1(A1g) (R) 554 cm–1

Fig. 7.3.6.

Normal modes and vibrational frequencies of XeF4 . Note that the x and y axes are equivalent, and only one component is shown for the degenerate modes. The coordinate system of locations of secondary twofold axes and mirror planes are shown in the lower part of the figure.

–

+

v2(B1g) (R) 524 cm–1

– v4(B2g) (R)

+

+ –

v3(A2u) (IR) 291 cm–1

+

+ v5(B2u)

v6(Eu) (IR)

218 cm–1

586 cm–1

v7(Eu) (R) 161 cm–1

y

C2''

σd

x C' 2 σv

Among the normal modes shown in Fig. 7.3.6, ν1 (A1g ), ν2 (B1g ), and ν6 (Eu ), are the stretching modes. It is appropriate here to note that it is straightforward to come up with these pictorial representations. If we call the four Xe–F bonds a, b, c, and d , the ν1 (A1g ) mode may be denoted as a + b + c + d , with “+” indicating contracting motion and “–” indicating stretching motion. The combination a +b+c+d is what we will get if we apply the projection operator P A1g to a. Similarly, if we apply P B1g to a, we will get a − b + c − d , which translates to ν2 (B1g ) in Fig. 7.3.6. If we apply P Eu to a, we get a − c; similarly, applying P Eu to b will yield b − d . When we combine these combination further, (a − c) ± (b − d ) are the results. One of these combinations is shown in Fig. 7.3.6, while the other is not. The stretching motions of a molecule can usually be derived in this manner. If the x and y axes are chosen to bisect the F–Xe–F bond angles, the symmetry of the normal modes is expressed as Γvib (XeF4 ) = A1g (R) + B1g (R) + B2g (R) + A2u (IR) + B1u + 2Eu (IR). (7.3.6)

Application of Group Theory to Molecular Systems As compared to eq. (7.3.5), the only difference is that the silent mode B2u in that expression is converted to B1u here, and now ν2 has B2g symmetry and ν4 has B1g symmetry. All deductions concerning infrared and Raman activities remain unchanged. Given the illustrations of the normal modes of a molecule, it is possible to identify their symmetry species from the character table. Each non-degenerate normal mode can be regarded as a basis, and the effects of all symmetry operations of the molecular point group on it are to be considered. For instance, the ν1 mode of XeF4 is invariant to all symmetry operations, i.e. R(ν1 ) = (1)ν1 for all values of R. Since the characters are all equal to 1, ν1 belongs to symmetry species A1g . For ν2 , the symmetry operation C4 leads to a character of −1, as shown below: C4

= (–1)

=

Working through all symmetry operations in the various classes by inspection, we can readily identify the symmetry species of ν2 as B1g . For a doubly degenerate normal mode, both components must be used together as the basis of a two-dimensional irreducible representation. For example, the operations C 2 and σ v on the two normal vibrations that constitute the ν6 mode lead to the character (sum of the diagonal elements of the corresponding 2×2 matrix) of −2 and 0, respectively, as illustrated below. Working through the remaining symmetry operations, the symmetry species of ν6 can be identified as Eu .

C2

σv

−1

0

0

−1

0

1

1

0

=

=

=

=

(5) SF4 As shown below, this molecule has C2v symmetry with two types of S–F bonds, equatorial and axial. The vibrational modes can be derived in the following way: C2v Γ (N0 ) f (R) Γ3N

E C2 5 1 3 −1 15 −1

σ v (xz) σ ,v (yz) 3 3 1 1 3 3

243

244

Symmetry in Chemistry

v1 (A1) (IR/R) 892 cm–1

v2 (A1) (IR/R) 559 cm–1

v3 (A1) (IR/R) 464 cm–1

+

– v5 (A2) (R) 414 cm–1

v4 (A1) (IR/R) 226 cm–1

v6 (B1) (IR/R) 730 cm–1 + –

Fig. 7.3.7.

Normal modes of SF4 and observed frequencies. The + and - symbols refer to motions of “coming out” and “going into” the paper, respectively.

v7 (B1) (IR/R) 532 cm–1

v8 (B2) (IR/R) 867 cm–1

– –

– v9 (B2) (IR/R) 353 cm–1

x

Fax Feq S

z Feq

Fax

y

Γ3N (SF4 ) = 5A1 + 2A2 + 4B1 + 4B2 .

Γvib (SF4 ) = 4A1 (IR/R) + A2 (R) + 2B1 (IR/R) + 2B2 (IR/R). So there are nine Raman lines and eight infrared lines. All eight infrared bands may be found in the Raman spectrum. The normal modes and their frequencies for SF4 are shown in Fig. 7.3.7. From this figure, it may be seen that stretching modes include ν1 (symmetric stretch for equatorial bonds), ν2 (symmetric stretch for axial bonds), ν6 (asymmetric stretch for axial bonds), and ν8 (asymmetric stretch for equatorial bonds). It is worth noting that we have so far discussed the vibrational spectra of three five-atom molecules: CF4 , XeF4 , and SF4 , with Td , D4h , and C2v symmetry, respectively. In their infrared spectra, two, three, and eight bands are observed, respectively. These results are consistent with the expectation that more symmetrical molecules have less infrared bands. (6) PF5 This well-known molecule assumes a trigonal bipyramidal structure with D3h symmetry. As in the case of SF4 , PF5 also has two types of bonds, equatorial and

Application of Group Theory to Molecular Systems

v1(A1' ) (R) 817 cm–1

v2(A1' ) (R) 640 cm–1

v3(A2") (IR) 944 cm–1

245

v4(A2") (IR) 575 cm–1

Fig. 7.3.8.

v5(E' ) (IR/R) 1026 cm–1

v6(E' ) (IR/R) 532 cm–1

v7(E' ) (IR/R) 300 cm–1

Normal modes of PF5 and their frequencies. Note that only one component is shown for each degenerate mode.

v8(E") (IR/R) 514 cm–1

axial P–F bonds. The vibrational modes for this molecule can be determined in the following way: D3h Γ (N0 ) f (R) Γ3N

E 2C 3 3C 2 6 3 2 3 0 −1 18 0 −2

σ h 2S 3 3σ v 4 1 4 1 −2 1 4 −2 4 ≡ 2A,1 + A,2 + 4E , + 3A,,2 + 2E ,,

Γvib (PF5 ) = 2A,1 (R) + 3E , (IR/R) + 2A,,2 (IR) + E ,, (R).

So there are five infrared and six Raman bands, three of which are coincident. The normal modes and their frequencies are shown in Fig. 7.3.8. From this figure, it is seen that ν1 (A,1 ) and ν5 (E , ) are the stretching modes for the equatorial bonds, while ν2 (A,1 ) and ν3 (A,,2 ) are the symmetric and asymmetric stretches for the axial bonds. Recall that in the derivation of the linear combinations for three equivalent functions a, b, and c, the results are a + b + c; 2a − b − c, and b − c, with the last two being degenerate. Mode ν1 (A,1 ) in Fig. 7.3.8 is equivalent to a + b + c, while ν5 (E , ) is 2a − b − c. The remaining combination, b − c, is not shown in this figure. (7) SF6 This highly symmetrical molecule has an octahedral structure with Oh symmetry. Contrary to SF4 and PF5 , where there are two types of bonds, all six bonds in SF6 are equivalent to each other. The vibrational modes of this molecule can be determined in the following manner: Oh Γ (N0 ) f (R) Γ3N

E 8C 3 7 1 3 0 21 0

6C 2 1 −1 −1

6C 4 3 1 3

3C 2 = C 24 3 −1 −3

i 6S 4 1 1 −3 −1 −3 −1

Γ3N (SF6 ) = A1g + Eg + T1g + T2g + 3T1u + T2u .

8S 6 1 0 0

3σ h 5 1 5

Γvib (SF6 ) = A1g (R) + Eg (R) + 2T1u (IR) + T2g (R) + T2u .

6σ d 3 1 3

246

Symmetry in Chemistry

v1(A1g) (R) 774 cm–1

v2(Eg) (R) 642 cm–1

v3(T1u) (R) 939 cm–1

v4(T1u) (IR) 614 cm–1

v5(T2g) (R) 523 cm–1

v3(T2u) 347 cm–1(estimated)

Fig. 7.3.9.

Normal modes of SF6 and their frequencies. Note that only one component is shown for each degenerate mode.

So there are three Raman and two infrared bands, none of which are coincident. Also, the T2u mode is silent. The normal modes and their frequencies are shown in Fig. 7.3.9. It is clear now that ν1 (A1g ), ν2 (Eg ), and ν3 (T1u ) are the stretching modes. If we call the six bonds a, b, . . ., f , with a and b colinear, and so are c and d , as well as e and f , then ν1 (A1g ) is equivalent to a+b+c+d+e+f; ν2 (Eg ) is equivalent to 2e+2f –a–b–c–d ; ν3 (T1u ) is equivalent to e − f . The ones not shown in Fig. 7.3.9 are the remaining component of Eg , a + b − c − d , and the last two components of T1u , a − b and c − d . These six combinations are identical to those listed in Table 7.1.5, the combinations of ligand orbitals in AH6 . 7.3.3

CO stretch in metal carbonyl complexes

In the previous examples for molecules with relatively few atoms, we studied and presented the results of all 3N −6 vibrations of the molecules. However, for molecules composed of a large number of atoms, often it is convenient to concentrate on a certain type of vibration. The prime example of this kind of investigation is the enumeration of the CO stretching modes in metal carbonyl complexes. Most metal carbonyl complexes exhibit sharp and intense CO bands in the range 1800–2100 cm−1 . Since the CO stretch motions are rarely coupled with other modes and CO absorption bands are not obscured by other vibrations, measurement of the CO stretch bands alone often provides valuable information about the geometric and electronic structures of the carbonyl complexes. As we may recall, free CO absorbs strongly at 2155 cm−1 , which corresponds to the stretching motion of a C≡O triple bond. On the other hand, most ketones and aldehyde exhibit bands near 1715 cm−1 , which corresponds formally to

Application of Group Theory to Molecular Systems σ-bond

M –

+

– π-bond

+

+

+ C

O

+

– C

M –

–

+

O

M

C

+

M

–

+

O

Fig. 7.3.10.

C

O

the stretching of a C=O double bond. In other words, the CO bonds in metal carbonyls have a bond order somewhere between 2 and 3. This observation may be rationalized by the simple bonding model illustrated in Fig. 7.3.10. The M–C σ bond is formed by donating the lone electrons on C to the empty dz2 orbital on M (upper portion of Fig. 7.3.10). The π bond is formed by back donation of the metal dπ electrons to the π ∗ orbital (introduced in Chapter 3) of CO. Populating the π ∗ orbital of CO tends to decrease the CO bond order, thus lowering the CO stretch frequency (lower portion of Fig. 7.3.10). These two components of metal-carbonyl bonding may be expressed by the two resonance structures "

M

C

O!

M

(I)

C

O

(II)

Thus structure (I), with higher CO frequencies, tends to build up electron density on M and is thus favored by systems with positive charges accumulated on the metal. On the other hand, structure (II), with lower CO frequencies, is favored by those with negative charge (which enhances back donation) on metal. In other words, net charges on carbonyl compounds have a profound effect on the CO stretch frequencies, as illustrated by the following two isoelectronic series: Importance of resonance structure − M–C≡O+ −→ ν (in cm−1 ) ν(A1g ) ν(Eg ) ν(T1u ) ν(A1 ) ν(T2 )

247

V(CO)− 6 2020 1895 1858

Cr(CO)6 2119 2027 2000

Mn(CO)+ 6 2192 2125 2095

Fe(CO)2− 4 1788 1786

Co(CO)− 4 2002 1888

Ni(CO)4 2125 2045

←− Importance of resonance structure M=C=O The identification of the symmetries of the CO stretching modes and the determination of their activities may be accomplished by the usual group theory techniques. Take the trigonal bipyramidal Fe(CO)5 (with D3h symmetry) as an example. The representation spanned by the five CO stretching motions, ΓCO , is once again derived by counting the number of CO groups unshifted by each operation in the D3h point group.

The σ and π bonding in metal carbonyls. Note that electrons flow from the shaded orbital to the unshaded orbital in both instances.

248

Symmetry in Chemistry O

O

C O

Fe

C

O

C

C

C

O

C

Fe

C

O

O

Fe

C

O

C

O

C

C

Carbonyl stretching modes and their frequencies for Fe(CO)5 . Note that only one component is shown for ν10 (E , ).

O

O

C

Fig. 7.3.11.

O

O v2(A&) 1 (R) 2030 cm–1

O

C

C

C

v1(A&) 1 (R) 2116 cm–1

O

C

Fe

C

O

O v6(A&&) 2 (IR) 2002 cm–1

C C

C

O

O

O v10(E&) (IR/R) 1979 cm–1 (IR); 1989 cm–1 (R)

O d C O

C

Fe

a

c

O

C C

C

b

e

O

O

D3h ΓCO

E 5

2C 3 2

3C 2 1

σh 3

2S 3 0

3σ v 3

ΓCO [Fe(CO)5 ] = 2A,1 (R) + A,,2 (IR) + E , (IR/R). So there are two and three CO stretch bands in the infrared and Raman spectra, respectively. The CO stretching modes and their frequencies are given in Fig. 7.3.11. The CO stretching modes shown in Fig. 7.3.11 may be easily obtained using the standard group theory technique. If we call the equatorial CO groups a, b, and c, and the axial groups d and e, the combinations for these five entities are simply A,1 , a+b+c; E , , 2a–b–c and b–c; A,1 , d +e; A,,2 , d –e; where + denotes stretching and – denotes contracting. Since there are two A,1 combinations, we can combine them further to form k(a+b+c)+d +e and k , (−a−b−c)+d +e, where k and k , are the combination coefficients. The stretching modes shown in Fig. 7.3.11 are simply graphical representations of these five linear combinations, except that one component of the E , mode, b − c, is not shown. Again, ν1 (A,1 ) is called the breathing mode, since all carbonyl groups are stretching and contracting

Application of Group Theory to Molecular Systems in unison. For metal-carbonyl complexes, the breathing mode often has the highest energy, as in the case of Fe(CO)5 . Now it is straightforward to show that, for tetrahedral carbonyl complexes M(CO)4 with Td symmetry, ΓCO [M(CO)4 ] = A1 (R) + T2 (IR/R). For octahedral carbonyl complexes M(CO)6 with Oh symmetry, ΓCO [M(CO)6 ] = A1g (R) + Eg (R) + T1u (IR). Since there is a direct relationship between the structure of a metal-carbonyl complex and the number of CO stretching bands, it is often possible to deduce the arrangement of the CO groups in a complex when we compare its spectrum with the number of CO stretch bands predicted for each of the possible structures using group theory techniques. As an illustrative example, consider the cis and trans isomers of an octahedral M(CO)4 L2 complex. For the trans isomer, with D4h symmetry, we have ΓCO [trans-M(CO)4 L2 ] = A1g (R) + B1g (R) + Eu (IR). So there are two CO stretching bands in the Raman spectrum and only one in infrared. Also, there are no coincident bands. For the cis isomer, with C2v symmetry, we have ΓCO [cis-M(CO)4 L2 ] = 2A1 (IR/R) + B1 (IR/R) + B2 (IR/R). So there are four infrared/Raman coincident lines for the cis isomer. When M is Mo and L is PCl3 , the trans isomer has indeed only one infrared CO stretch band, while there are four for the cis isomer. These results are summarized in Fig. 7.3.12, along with the pictorial illustrations of the CO stretching modes. It appears that the two A1 modes of the cis isomer do not couple strongly. Also, this is another example for the general rule that a more symmetrical molecule will have fewer infrared bands. In some cases, two isomers may have the same number of CO stretching bands, yet they may still be distinguished by the relative intensities of the bands. Take the cis- and trans-[(η5 -C5 H5 )Mo(CO)2 PPh3 C4 H6 O]+ and their spectra as an example. The structural formulas of these complex ions and their infrared spectra are shown in Fig. 7.3.13. In both spectra, the two bands are the symmetric and asymmetric CO stretch modes. As shown in the previous example of cis-[Mo(CO)4 (PCl3 )2 ], the symmetric modes has a slightly higher energy. Also, as shown below, the intensity ratio is related to the angle formed by the two groups. Referring to Fig. 7.3.14, the dipole vector R for a stretching mode is simply the sum or difference of the two individual CO group dipoles. Since the inten2 sities of the symmetric and asymmetric stretches are proportional to Rsym and

249

250

Symmetry in Chemistry O C cis:

C

O C

O

C O

L

C O

L

C O

L (1)

C trans: O C Fig. 7.3.12.

O

CO stretching modes and their infrared bands of cis- and trans-[Mo(CO)4 (PCl3 )2 ].

C O

L

v(A1 ) (IR/R) 2004 cm–1 L

O

C

C O O C C v(A1g) (R)

C

C O O C O

L

v(B2) (IR/R) 1986 cm–1 L

O

C

C O O C C

O

L

v(B1g) (R)

C

Ph3P

O C O

C L

v(Eu) (IR) 1896 cm–1

+

+ O

C O

L

L

O

O

C

C O

v(B1) (IR/R) 2004 cm–1

C

O

L

O C

O

C O L

(2)

v(A1 ) (IR/R) 2072 cm–1

C

L

C O

L

L

O C

O

C

Mo

OC

CO CO

Ph3P

(2)

(1)

C

O

OC

Absorbance

0.10

(1)

0.30

(2)

0.50 0.70 1.00 2.00

Fig. 7.3.13.

The CO stretching bands and their relative intensities of the cis and trans isomers of [(η5 –C5 H5 )Mo(CO)2 PPh3 C4 H6 O]+ .

2200 2000 1800

M

r

Fig. 7.3.14.

Diagram showing how the two CO dipoles (r) are combined to give dipole vector R for the M(CO)2 moiety. Different ways of combining lead to Rsym and Rasym .

2200 2000 1800 v/cm–1

r

C

2θ

C

r

r Rsym

Rsym = 2r cosθ

r

r Rasym

Rasym = 2r sinθ

Application of Group Theory to Molecular Systems 2 Rasym , respectively, the ratio of these two intensities is simply 2 2 /Rasym I (1)/I (2) = Rsym

= (2r cos θ 2 )/(2r sin θ)2 = cot 2 θ,

where 2θ is the angle formed by the two CO groups. For the left spectrum in Fig. 7.3.13, I (1)/I (2) = 1.44, and 2θ is 79◦ , indicating this spectrum is that of the cis isomer. For the spectrum on the right, I (1)/I (2) = 0.32, and 2θ is 121◦ , signifying this spectrum is that of the trans isomer. In polynuclear carbonyls, i.e., those carbonyl complexes with two or more metal atoms, the CO ligands may bond to the metal(s) in different ways. In addition to the terminal carbonyl groups, those we have studied so far, we may also have µn bridging carbonyls, which bond to n metal atoms. In the case of µ2 bridging, it may be assumed that a CO group donates one electron to each metal. Also, both metals back-donate to the CO ligand, thus leading to vibrational frequencies lower than those of terminal COs. Indeed, most µ2 bridging CO groups absorb in the range of 1700–1860 cm−1 . In the following we consider the dinulclear complex Co2 (CO)8 which, in the solid state, has the following structure with C2v symmetry: OC

CO

CO

CO z

OC

CO CO

OC

y x

To derive the CO stretching modes, we may consider the bridging and terminal groups separately. C2v (ΓCO )brid (ΓCO )term

E 2 6

C2 0 0

σ v (xz) σ ,v (yz) 0 2 2 0

(ΓCO )brid [Co(CO)8 ] = A1 (IR/R) + B2 (IR/R),

(ΓCO )term [Co(CO)8 ] = 2A1 (IR/R) + A2 (R) + 2B1 (IR/R) + B2 (IR/R).

So there are seven CO stretching bands in the infrared spectrum, as found experimentally. The terminal CO stretching frequencies are at 2075, 2064, 2047, 2035, and 2028 cm−1 , and the two bridging CO stretch peaks are at 1867 and 1859 cm−1 .

251

252

Symmetry in Chemistry As another example, consider the highly symmetrical Fe2 (CO)9 , with D3h symmetry, as shown above. The symmetries of the CO stretching modes can be determined readily: D3h (ΓCO )brid (ΓCO )term

E 3 6

2C 3 0 0

3C 2 1 0

σh 3 0

2S 3 0 0

3σ v 1 2

(ΓCO )brid [Fe2 (CO)9 ] = A,1 (R) + E , (IR/R),

(ΓCO )term [Fe2 (CO)9 ] = A,1 (R) + A,,2 (IR) + E , (IR/R) + E ,, (R).

So there are three infrared absorption bands: 2066 (A,,2 ), 2038 (E , , terminal), and 1855 (E , , bridging) cm−1 . In this section, using purely qualitative symmetry arguments, we have discussed the kind of information regarding structure and bonding we can obtain from vibrational spectroscopy. Obviously, treatments of this kind have their limitations, such as their failure to make reliable assignments for the observed vibrational bands. To carry out this type of tasks with confidence, we need to make use of quantitative methods, which are beyond the scope of this book. 7.3.4

Linear molecules

In this section, we examine the vibrational spectra of a few linear molecules to illustrate the principles we have discussed. (1) Hydrogen cyanide and carbon dioxide Both HCN and CO2 , with C∞v and D∞h symmetry, respectively, have two bonds and, hence, have two stretching modes and one (doubly degenerate) bending mode. In CO2 , the two bonds are equivalent and they may couple in a symmetric and an antisymmetric way, giving rise to symmetric and asymmetric stretching modes. However, for HCN, we simply have the C–H and C≡N stretching modes. The observed frequencies and their assignments for these two triatomic molecules are summarized in Tables 7.3.1 and 7.3.2. Table 7.3.1. The normal modes of HCN and their observed

frequencies Symmetry

cm−1

Normal mode

Activity

Description

=

712

H

C

N

IR/R

bending

25%

mostly electrostatic X–H < H· · · Y 150–220 250–320 130◦ –180◦ 15–50 10 ∼25%

electrostatic X–H 763 K anti-CaF2 structure

Yellow mp > 840 K anti-CaF2 structure

Orange mp 763 K anti-CdCl2 structure

Peroxides M2 O2

Colorless dec. > 473 K —

Pale yellow dec. ≈ 948 K

Yellow dec. ≈ 763 K

Yellow dec. ≈ 843 K

Yellow dec. ≈ 863 K

Orange dec. ≈573 K NaCl-structure

Orange mp 653 K dec. ≈ 673 K CaC2 structure Dark red dec. at room temp. CsCl structure —

Orange mp 685 K CaC2 structure

Orange mp 705 K CaC2 structure

Dark red dec. ≈ room temp. CsCl structure Rb6 O Bronze color dec. 266 K Rb9 O2 Copper color mp 313 K

Dark red dec. > 323 K CsCl structure

Superoxides MO2

Ozonides MO3

—

Red dec. Na > K > Rb > Cs, and this is frequently observed. (b) The electrostatic association favors the formation of the M+ X− ion pairs, and it is inevitable that such ion pairs will associate, so as to delocalize the electronic charges. The most efficient way of accomplishing this is by ring formation. If the X− groups are relatively small and for the most part coplanar with the ring, then stacking of rings can occur. For example, two dimers are connected to give a cubane-like tetramer, and two trimers lead to a hexagonal prismatic hexamer. (c) In the ring structures, the bond angles at X− are acute. Hence the formation of larger rings would reduce repulsion between X− ions and between M+ ions. (d) Since the alkali metal complexes are mostly discrete molecules with an ionic core surrounded by organic peripheral groups, they have relatively low melting points and good solubility in weakly polar organic solvents. These properties have led to some practical applications; for example, lithium

Alkali and Alkaline-Earth Metals (a)

(b)

437

(c)

Li Li

R O

R

Li O

THF

(d)

O THF

(e)

Fig. 12.2.4.

Li

Li O

O

C

C

complexes are used as low-energy electrolytic sources of metals, in the construction of portable batteries, and as halogenating agents and specific reagents in organic syntheses.

(2) Lithium alkoxides and aryloxides Anionic oxygen donors display a strong attraction for Li+ ions and usually adopt typical structures of their aggregation state, as shown in Figs 12.2.4(a)-(c). Figure 12.2.4(a) shows the dimeric structure of [Li(THF)2 OC(NMe2 )(c-2,4,6C7 H6 )]2 , in which Li+ is four-coordinated by the oxygen atoms from two THF ligands and two alkoxides OC(NMe2 )(c-2,4,6-C7 H6 ). The Li–O distances are 188 and 192 pm for the bridging oxygen of the enolate, and 199 pm for THF. Figure 12.2.4(b) shows the tetrameric cubane-type structure of [Li(THF)OC(CHt Bu)OMe]4 . The Li–O distances are 196 pm (enolate) and 193 pm (THF). Figure 12.2.4(c) shows the hexagonal-prismatic structure of [LiOC(CH2 )t Bu]6 . The Li–O distances are 190 pm (av.) in the six-membered ring of one stack, and 195 pm (av.) between the six-membered rings. Figures 12.2.4(d) and (e) show the structures of (LiOPh)2 (18-crown-6) and [(LiOPh)2 (15-crown-5)]2 . In the former, there is a central dimeric (Li–O)2 unit. Owing to its larger size, 18-crown-6 can coordinate both Li+ ions, each through three oxygen atoms (Li–O 215 pm, av.). These Li+ ions are bridged by phenoxide groups (Li–O 188 pm). The structure of the latter has a very similar (LiOPh)2 core (Li–O 187 and 190 pm). Each Li+ ion is coordinated to another –OPh group as well as one ether oxygen from a 15-crown-5 donor. This ether oxygen atom also connected to a further Li+ ion whose coordination is completed by the remaining four oxygen donors of the 15-crown-5 ligands.

Core structures of some lithium alkoxides and aryloxides: (a) [Li(THF)2 OC(NMe2 )(c-2,4,6C7 H6 )]2 , (b) [Li(THF)OC(CHt Bu)OMe]4 , (c) [LiOC(CH2 )t Bu]6 , (d) (LiOPh)2 (18-crown-6), and (e) [(LiOPh)2 (15-crown-5)]2 .

438

Structural Chemistry of Selected Elements (a)

(b) Li Li N

N (d)

(c)

(e) Si

N

N Li

Li

N Li

Im

(f)

THF

Im

Fig. 12.2.5.

Core structures of some lithium amides and imides: (a) (LiTMP)4 , (b) Li4 (TMEDA)2 [c-N(CH2 )4 ], (c) [Li{c-N(CH2 )6 }]6 , (d) [{LiN(SiMe3 )}3 SiR]2 , (e) [LiNHt Bu]8 , and (f) [Li12 O2 Cl2 (ImN)8 (THF)4 ]·8(THF).

Im

THF

Im Im

O

Im

Cl

Im = 1,3-dimethylimidazol-2-ylidene THF = tetrahydrofuran

Li THF N

THF

Im Im

(3) Lithium amides The structures of lithium amides are characterized by a strong tendency for association. Monomeric structures are observed only in the presence of very bulky groups at nitrogen and/or donor molecules that coordinate strongly to lithium. In the dimeric lithium amides, the Li+ ion is usually simultaneously coordinated by N atoms and other atoms. The trimer [LiN(SiMe3 )2 ]3 has a planar cyclic arrangement of its Li3 N3 core. The Li–N bonds are 200 pm long with internal angles of 148◦ at Li and 92◦ at N (average values). Figure 12.2.5 shows the structures of some higher aggregates of lithium amides. (a) The tetramer (LiTMP)4 (TMP = 2,2,6,6-tetramethylpiperidinide) has a planar Li4 N4 core with a nearly linear angle (168.5◦ ) at Li and an internal angle of 101.5◦ at N. The average Li–N distance is 200 pm, as shown in Fig. 12.2.5(a). (b) The tetrameric molecule Li4 (TMEDA)2 [c-N(CH2 )4 ] (TMEDA = N ,N , tetramethylenediamine) has a ladder structure in which adjacent Li2 N2 rings share edges with further aggregation blocked by TMEDA coordination, as shown in Fig. 12.2.5(b). (c) The hexameric [Li{c-N(CH2 )6 }]6 has a stacked structure, as shown in Fig. 12.2.5(c). This involves the association of two [Li-c-N(CH2 )6 ]3 units to form a hexagonal-prismatic Li6 N6 unit, in which all N atoms have the relatively rare coordination number of five. (d) The basic framework in [{LiN(SiMe3 )}3 SiR]2 (R = Me, t Bu and Ph) is derived from the dimerization of a trisamidosilane. It exhibits molecular

Alkali and Alkaline-Earth Metals

439

D3d symmetry, as shown in Fig. 12.2.5(d). Each of the three Li+ ions in a monomeric unit is coordinated by two N atoms in a chelating fashion, and linkage of units occurs through single Li–N contacts. This causes all N atoms to be five-coordinate, which leads to weakening of the Li–N and Si–N bonds. (e) Figure 12.2.5(e) shows the core structure of [LiNHt Bu]8 , in which planar Li2 N2 ring units are connected to form a discrete prismatic ladder molecule. (f) Figure 12.2.5(f) shows the centrosymmetric core structure of [Li12 O2 Cl2 (ImN)8 (THF)4 ]·8(THF), which consists of a folded Li4 N2 O2 ladder in which the central O2− 2 ion is connected to two Li centers. The two adjacent Li4 ClN3 ladders are connected with the central Li4 N2 O2 unit via Li–O, Li–Cl and Li–N interactions. The bond distances are Li–N

195.3–218.3 pm,

Li–O

191.7–259.3 pm,

Li–Cl

238.5–239.6 pm,

O–O

154.4 pm.

In this structure, Li atoms are four-coordinated, and N atoms are four- or five-coordinated. (4) Lithium halide complexes In view of the very high lattice energy of LiF, there is as yet no known complex that contains LiF and a Lewis base donor ligand. However, a range of crystalline fluorosilyl-amide and -phosphide complexes that feature significant Li· · · F contacts have been synthesized and characterized. For example, {[t Bu2 Si(F)]2 N}Li ·2THF has a heteroatomic ladder core, as shown in Fig. 12.2.6(a), and dimeric [t Bu2 SiP(Ph)(F)Li)·2THF]2 contains an eight-membered heteroatomic ring. A large number of complexes containing the halide salts LiX (X = Cl, Br, and I) have been characterized in the solid state. The structures of some of these complexes are shown in Figs. 12.2.6(b)-(f). In the center of the cubane complex [LiCl·HMPA]4 (HMPAis (Me2 N)3 P=O), each Li+ is bonded to three Cl− and one oxygen of HMPA, as shown in Fig. 12.2.6(b). The complex (LiCl)6 (TMEDA)2 has a complicated polymeric structure based on a (LiCl)6 core, as shown in Fig. 12.2.6(c). Tetrameric [LiBr]4 ·6[2,6-Me2 Py] has a staggered ladder structure, as shown N Si Li

F

Li

Li (a)

(b)

(c)

Fig. 12.2.6.

(f)

Structures of some lithium halide complexes: (a) {[t Bu2 Si(F)]2 N}Li ·2THF, (b) [LiCl·HMPA]4 , (c) (LiCl)6 (TMEDA)2 , (d) [LiBr]4 ·6[2,6-Me2 Py], (e) [Li6 Br4 (Et2 O)10 ]2+ , and (f) [LiBr·THF]n .

Br

Li

Br

Li

Br (d)

Cl

Cl

(e)

Li

440

Structural Chemistry of Selected Elements in Fig. 12.2.6(d). In the complex [Li6 Br4 (Et2 O)10 ]2+ ·2[Ag3 Li2 Ph6 ]− , the hexametallic dication contains a Li6 Br4 unit which can be regarded as two three-rung ladders sharing their terminal Br anions, as shown in Fig. 12.2.6(e). The structure of oligomeric [LiBr·THF]n is that of a unique corrugated ladder, in which [LiBr]2 units are linked together by µ3 -Br bridges, as shown in Fig. 12.2.6(f). Polymeric ladder structures have also been observed for a variety of other alkali metal organometallic derivatives. (5) Lithium salts of heavier heteroatom compounds Lithium can be coordinated by heavier main-group elements, such as S, Se, Te, Si, and P atoms, to form complexes. In the complex [Li2 (THF)2 Cp*TaS3 ]2 , the monomeric unit consists of a pair of four-membered Ta–S–Li–S rings sharing a common Ta–S edge. Dimerization occurs through further Li–S linkages, affording a hexagonal-prismatic skeleton, as shown in Figure 12.2.7(a). The bond lengths are Li–S 248 pm(av.) and Ta–S 228 pm(av.). Figure 12.2.7(b) shows the core structure of Li(THF)3 SeMes* (Mes* = 2,4,6-C6 H2 R3 , where R is a bulky group such as But ) which has Li–Se bond length 257 pm. Figure 12.2.7(c) shows the core structure of the dimeric complex [Li(THF)2 TeSi(SiMe3 )3 ]2 , in which the distances of bridging Li–Te bonds are 282 and 288 pm. Some lithium silicide complexes have been characterized. The complex Li(THF)3 SiPh3 displays a terminal Li–Si bond that has a length of 267 pm, which is the same as that in Li(THF)3 Si(SiMe3 ). Figure 12.2.7(d) shows the core structure of Li(THF)3 SiPh3 . There is no interaction between Li and the phenyl rings. The C–Si–C bond angles are smaller (101.3◦ av.) than the ideal tetrahedral value, while the Li–Si–C angles are correspondingly larger (116.8◦ av.). This indicates the existence of a lone pair on silicon.

Se

Li Li (b)

O

(c)

Te

O

Ta Li S

Fig. 12.2.7.

Core structures of some lithium complexes bearing heavier heteroatom ligands: (a) [Li2 (THF)2 Cp*TaS3 ]2 , (b) Li(THF)3 SeMes*, (c) [Li(THF)2 TeSi(SiMe3 )3 ]2 , (d) Li(THF)3 SiPh3 , (e) Li(Et2 O)2 (P t Bu)2 (Ga2t Bu3 ), (f) [Li(Et2 O)PPh2 ]n , (g) [LiP(SiMe3 )2 ]4 (THF)2 .

Li

O

O

(a)

(d)

Si

Ga

O P

Li

(e)

P

Li

Li

P

O (f)

(g)

O

Alkali and Alkaline-Earth Metals

441

Figures 12.2.7(e)–(g) show the core structures of three lithium phosphide complexes. Li(Et2 O)2 (Pt Bu)2 (Gat2 Bu3 ) has a puckered Ga2 P2 four-membered ring, in which one Ga atom is four- and the other three-coordinated, as shown in Fig. 12.2.7(e). The Li–P bond length is 266 pm(av.). The polymeric complex [Li(Et2 O)PPh2 ]n has a backbone of alternating Li and P chain, as shown in Fig. 12.2.7(f). The bond length of Li–P is 248 pm (av.) and Li–O is 194 pm (av.). Figure 12.2.7(g) shows the core structure of [LiP(SiMe3 )2 ]4 (THF)2 , which has a ladder structure with Li–P bond length 253 pm(av.). (6) Sodium coordination complexes Recent development in the coordination chemistry of Group 1 elements has extended our knowledge of their chemical behavior and provided many interesting new structural types. Three examples among known sodium coordination complexes are presented below: (a) A rare example of a bimetallic imido complex is the triple-stacked Li4 Na2 [N=C(Ph)(t Bu)]6 . This molecule has six metal atoms in a triplelayered stack of four-membered M2 N2 rings, with the outer rings containing lithium and the central ring containing sodium. In the structure, lithium is three-coordinated and sodium is four-coordinated, as shown in Fig. 12.2.8(a). (b) The large aggregate [Na8 (OCH2 CH2 OCH2 CH2 OMe)6 (SiH3 )2 ] has been prepared and characterized. The eight sodium atoms form a cube, the faces of which are capped by the alkoxo oxygen atoms of the six (OCH2 CH2 OCH2 CH2 OMe) ligands, which are each bound to four sodium atoms with Na–O distances in the range 230–242 pm. The sodium and oxygen atoms constitute the vertices of an approximate rhombododecahedron. Six of eight sodium atoms are five-coordinated by oxygen atoms, and each of the other two Na atoms is bonded by a SiH− 3 group, which has inverted C3v symmetry with Na–Si–H bond angles of 58◦ –62◦ , as shown in Fig. 12.2.8(b).

(a)

Si

(b)

H Na

N Li Na

Fig. 12.2.8.

Na H Si

O

Structures of (a) Li4 Na2 [N=C(Ph)(t Bu)]6 (the Ph and t Bu groups are not shown), and (b) [Na8 (OCH2 CH2 OCH2 CH2 OMe)6 (SiH3 )2 ].

442

Structural Chemistry of Selected Elements

O

Bu

Na H

Fig. 12.2.9.

Structure of [Na11 (Ot Bu)10 (OH)].

Despite the strange appearance of the SiH− 3 configuration in this complex, ab initio calculations conducted on the simplified model compound (NaOH)3 NaSiH3 indicate that the form with inverted hydrogens is 6 kJ mol−1 lower in energy than the un-inverted form. The results suggest that electrostatic interaction, rather than agostic interaction between the SiH3 group and its three adjacent Na neighbors, stabilizes the inverted form. (c) The complex [Na11 (Ot Bu)10 (OH)] is obtained from the reaction of sodium tert-butanolate with sodium hydroxide. Its structure features a 21-vertex cage constructed from eleven sodium cations and ten tert-butanolate anions, with an encapsulated hydroxide ion in its interior, as shown in Fig. 12.2.9. In the lower part of the cage, eight sodium atoms constitute a square antiprism, and four of the lower triangular faces are each capped by a µ3 -Ot Bu group. The Na4 square face at the bottom is capped by a µ4 -Ot Bu group, and the upper Na4 square face is capped in an inverted fashion by the µ4 -OH− group. Thus the OH− group resides within a Na8 -core, and it also forms an O–H· · · O hydrogen bond of length 297.5 pm. The Na–O distances in the 21-vertex cage are in the range of 219–43 pm. 12.3

Structure and bonding in organic alkali metal compounds

12.3.1

Methyllithium and related compounds

Lithium readily interacts with hydrocarbon π systems such as olefins, arenes, and acetylenes at various sites simultaneously. Lithium reacts with organic halides to give alkyllithium or aryllithium derivatives in high yield. Therefore, a wide variety of organolithium reagents can be made. These organolithium compounds are typically covalent species, which can be sublimed, distilled in a vacuum, and dissolved in many organic solvents. The Li–C bond is a strong polarized covalent bond, so that organolithium compounds serve as sources

Alkali and Alkaline-Earth Metals

443

(b)

(a)

Fig. 12.3.1.

Li Li CH3

H C

of anionic carbon, which can be replaced by Si, Ge, Sn, Pb, Sb, or Bi. When Sn(C6 H5 )3 or Sb(C6 H11 )2 groups are used to replace CH3 , CMe3 or C(SiMe3 )3 in organolithium compounds, new species containing Li–Sn or Li–Sb bonds are formed. Methyllithium, the simplest organolithium compound, is tetrameric. The Li4 (CH3 )4 molecule with Td symmetry may be described as a tetrahedral array of four Li atoms with a methyl C atom located above each face of the tetrahedron, as shown in Fig. 12.3.1(a). The bond lengths are Li–Li 268 pm and Li–C 231 pm, and the bond angle Li–C–Li is 68.3◦ . Vinyllithium, LiHC=CH2 , has a similar tetrameric structure in the crystalline state with a THF ligand attached to each lithium atom [Fig. 12.3.1(b)]. In THF solution vinyllithium is tetrameric as well. The internuclear Li–H distances are in agreement with those calculated from the two-dimensional NMR 6 Li, 1 H HOSEY spectra. When steric hindrance is minimal, organolithium compounds tend to form tetrameric aggregates with a tetrahedral Li4 core. Figures 12.3.2(a)–(d) show the structures of some examples: (a) (LiBr)2 ·(CH2 CH2 CHLi)2 ·4Et2 O, (b) (PhLi·Et2 O)3 ·LiBr, (c) [C6 H4 CH2 N(CH3 )2 Li]4 , and (d) (t BuC≡CLi)4 (THF)4 . In these complexes, the Li–C bond lengths range from 219 to 253 pm, with an average value of 229 pm, while the Li–Li distances lie in the range 242–263 pm (average 256 pm). The Li–C bond lengths are slightly longer than those for the terminally bonded organolithium compounds. This difference may be attributed to multicenter bonding in the tetrameric structures. 12.3.2

π-Complexes of lithium

The interactions between Li atom and diverse π systems yield many types of lithium π complexes. Figures 12.3.3(a)–(c) show the schematic representation of the core structures of some π complexes of lithium, and Fig. 12.3.3(d) shows the molecular structure of [C2 P2 (SiMe3 )2 ]2− ·2[Li+ (DME)] (DME = dimethoxyethane). (a) Li[Me2 N(CH2 )2 NMe2 ]·[C5 H2 (SiMe3 )3 ]: In the cyclopentadienyllithium complex, the Li atom is coordinated by the planar Cp ring and by one chelating TMEDA ligand. The Li–C distances are 226 to 229 pm (average value 227 pm). (b) Li2 [Me2 N(CH2 )2 NMe2 ]·C10 H8 : In the naphthalene–lithium complex, each Li atom is coordinated by one η6 six-membered ring and a chelating TEMDA ligand. The two Li atoms are not situated directly opposite to

Molecular structure of (a) methyllithium tetramer (Li4 Me4 ) (H atoms have been omitted); and (b) vinyllithium·THF tetramer (LiHC=CH2 ·THF)4 (THF ligands have been omitted).

444

Structural Chemistry of Selected Elements (a)

(b)

Br

Li Br

(c)

Li

O

O

(d)

Fig. 12.3.2.

Structures of some organolithium complexes: (a) (LiBr)2 ·(CH2 CH2 CHLi)2 ·4Et2 O, (b) (PhLi·Et2 O)3 ·LiBr, (c) [C6 H4 CH2 N(CH3 )2 Li]4 , and (d) (t BuC≡CLi)4 (THF)4 .

Li (CH3)2N

O

Li

Li

Li (a)

(b)

O Li P Fig. 12.3.3.

Structures of some lithium π complexes: (a) Li[Me2 N(CH2 )2 NMe2 ]·[C5 H2 (SiMe3 )3 ], (b) Li2 [Me2 N(CH2 )2 NMe2 ]·C10 H8 , (c) Li2 [Me2 N(CH2 )2 NMe2 ][H2 C=CH– CH=CH–CH=CH2 ], and (d) [C2 P2 (SiMe3 )2 ]2− ·2[Li+ (DME)].

Si Li

(c)

(d)

each other. The Li–C distances are in the range 226–66 pm; the average value is 242 pm. (c) Li2 [Me2 N(CH2 )2 NMe2 ][H2 C=CH–CH=CH–CH=CH2 ]: In this complex, each Li atom is coordinated by the bridging bistetrahaptotriene and by one chelating TMEDA ligand. The Li–C distances are 221 to 240 pm (average value 228 pm).

Alkali and Alkaline-Earth Metals

445

(a)

Na(2)

Na(1)

(b)

(c) Fig. 12.3.4.

Na K

(d) [C2 P2 (SiMe3 )2 ]2− ·2[Li+ (DME)]: In this complex, the C2 P2 unit forms a planar four-membered ring, which exhibits aromatic properties with six π electrons. The two Li atoms are each coordinated to the central η4 -C2 P2 ring. The distances of Li–C and Li–P are 239.1 and 245.8 pm, respectively. Each Li atom is also coordinated by one chelating DME ligand.

12.3.3

π -Complexes of sodium and potassium

Many π complexes of sodium and potassium have been characterized. The Na and K atoms of these complexes are polyhapto-bonded to the ring π systems, and frequently attached to two or more rings to give infinite chain structures. Figure 12.3.4 shows the structures of some π complexes of sodium and potassium. In the structure of Na2 [Ph2 C=CPh2 ]·2Et2 O, the two halves of the [Ph2 C=CPh2 ]2− dianion twist through 56◦ relative to each other, and the central C=C bond is lengthened to 149 pm as compared to 136 pm in Ph2 C=CPh2 . The coordination of Na(1) involves the >C=C< π bond and two adjacent π bonds. The two Et2 O ligands are also coordinated to it. The Na(2) is sandwiched between two phenyl rings in a bent fashion, and further interacts with a π bond in the third ring, as shown in Fig. 12.3.4(a). The Na(1)–C and Na(2)–C distances lie in the ranges 270–282 pm and 276–309 pm, respectively. Figure 12.3.4(b)–(c) show the structures of Na(C5 H5 )(en) and K[C5 H4 (SiMe3 )], respectively. In these complexes, each metal (Na or K) atom is centrally positioned between two bridging cyclopentadienyl rings, leading to a bent sandwich polymeric zigzag chain structure. The sodium atom is further coordinated by an ethylenediamine ligand, and the potassium atom interacts with an additional Cp ring of a neighboring chain.

Structures of some π complexes of sodium and potassium: (a) Na2 [Ph2 C=CPh2 ]·2Et2 O, (b) Na(C5 H5 )(en), and (c) K[C5 H4 (SiMe3 )].

446

Structural Chemistry of Selected Elements 12.4

Alkalides and electrides

12.4.1

Alkalides

The alkali metals can be dissolved in liquid ammonia, and also in other solvents such as ethers and organic amines. Solutions of the alkali metals (except Li) contain solvated M− anions as well as solvated M+ cations: 2M(s) ? A M+ (solv) + M− (solv). Successful isolation of stable solids containing these alkalide anions depends on driving the equilibrium to the right and then on protecting the anion from the polarizing effects of the cation. Both goals have been realized by using macrocyclic ethers (crown ethers and cryptands). The oxa-based cryptands such as 2.2.2-crypt (also written as C222) are particularly effective in encapsulating M+ cations. Alkalides are crystalline compounds that contain the alkali metal anions, M− (Na− , K− , Rb− , or Cs− ). The first alkalide compound Na+ (C222)·Na− was synthesized and characterized by Dye in 1974. Elemental sodium dissolves only very slightly (∼ 10−6 mol L−1 ) in ethylamine, but when C222 is added, the solubility increases dramatically to 0.2 mol L−1 , according to the equation 2Na(s) + C(222) −→ Na+ (C222) + Na− . When cooled to –15 ◦ C or below, the solution deposits shiny, gold-colored thin hexagonal crystals of [Na+ (C222)]·Na− . Single-crystal X-ray analysis shows that two sodium atoms are in very different environments in the crystal. One is located inside the cryptand at distances from the nitrogen and oxygen atoms characteristic of a trapped Na+ cation. The other is a sodium anion (natride), Na− , which is located far away from all other atoms. Figure 12.4.1 shows the cryptated sodium cation with its six nearest natrides in the crystals. The close analogy of the natride ion with an iodide ion is brought out clearly by comparing [Na+ (C222)]·Na− with [Na+ (C222)]·I− .

Na+ N Fig. 12.4.1.

The cryptated sodium cation surrounded by six natride anions in crystalline [Na+ (C222)]·Na− .

Na–

O C

Alkali and Alkaline-Earth Metals Table 12.4.1. Radii of alkali metal anions from structure of alkalides and alkali metals∗

Compound

rM− (min) (pm)

rM− (av ) (pm)

datom (pm)

rM+ (pm)

— 255 234 260 248 235 — 294 277 — 300 299 264 — 317 309

— 273 (14) 264 (16) 289 (16) 277 (10) 279 (8) — 312 (10) 314 (16) — 321 (14) 323 (9) 306 (16) — 350 (15) 346 (15)

372

95

277

463

133

330

485

148

337

527

167

360

Na metal K+ (C222)·Na− Cs+ (18C6)·Na− Rb+ (15C5)2 ·Na− K+ (HMHCY)·Na− Cs+ (HMHCY)·Na− K metal K+ (C222)·K− Cs+ (15C5)2 ·K− Rb metal Rb+ (C222)·Rb− Rb+ (18C6)·Rb− Rb+ (15C5)2 ·Rb− Cs metal Cs+ (C222)·Cs− Cs+ (18C6)2 ·Cs−

rM− (pm)

∗

HMHCY stands for hexamethyl hexacyclen, which is the common name of 1,4,7,10,13,16-hexaaza1,4,7,10,13,16-hexamethyl cyclooctadecane. Here rM −(min) is the distance between an anion and its nearest hydrogen atoms minus the van der Waals radius of hydrogen (120 pm), while rM −(av) is the average radius over the nearest hydrogen atoms; the numbers in the brackets are the numbers of hydrogen atoms for averaging. Similarly, datom is the interatomic distance in the metal; rM− is equal to datom minus rM+ .

More than 40 alkalide compounds that contain the anions Na− , K− , Rb− , or Cs− have been synthesized, and their crystal structures have been determined. Table 12.4.1 lists the calculated radii of alkali metal anions from structures of alkalides and alkali metals. The values of rM− (av) derived from alkalides and rM− from the alkali metals are in good agreement. 12.4.2

Electrides

The counterparts to alkalides are electrides, which are crystalline compounds with the same type of complexed M+ cations, but the M− anions are replaced by entrapped electrons that usually occupy the same sites. The crystal structures of several electrides are known: Li+ (C211)e− , K+ (C222)e− , Rb+ (C222)e− , Cs+ (18C6)2 e− , Cs+ (15C5)2 e− , and [Cs+ (18C6)(15C5)e− ]6 (18C6). Comparison of the structures of the complexed cation in the natride Li+ (C211)Na− and the electride Li+ (C211)e− shows that the geometric parameters are virtually identical, as shown in Fig. 12.4.2, supporting the assumption that the “excess” electron density in the electride does not penetrate substantially into the cryptand cage. In Cs+ (18C6)2 Na− and Cs+ (18C6)2 e− , not only are the complexed cation geometries the same, but the crystal structures are also very similar, the major difference being a slightly larger anionic site for Na− than for e− . Electrides made with crown ethers and oxa-based cryptands are generally unstable above −40 ◦ C, since the ether linkages are vulnerable to electron capture and reductive cleavage. Using a specifically designed pentacyclic tripiperazine cryptand TripPip222 [molecular structure displayed

447

448

Structural Chemistry of Selected Elements (a)

(b)

N N Li+

Li+ Fig. 12.4.2.

Comparison of the structures of the complexed cation in (a) Li+ (C211)Na− and (b) Li+ (C211)e− .

C

C

O

O

in Fig. 12.4.3(a)], the pair of isomorphous compounds Na+ (TripPip222)Na− and Na+ (TripPip222)e− have been synthesized and fully characterized. This air-sensitive electride is stable up to about 40 ◦ C before it begins to decompose into a mixture of the sodide and the free complexant. While the trapped electron could be viewed as the simplest possible anion, there is a significant difference between alkalides and electrides. Whereas the large alkali metal anions are confined to the cavities, only the probability density of a trapped electron can be defined. The electronic wavefunction can extend into all regions of space, and electron density tends to seek out the void spaces provided by the cavities and by intercavity channels.

N N

(a) Structural formula of the complexant 1,4,7,10,13,16,21,24-octaazapentacyclo [8.8.8.24,7.213,16.221,24]dotriacontane (TriPip222). (b) The “ladder-like” zigzag chain of cavities S and channels A and B, along the a direction (horizontal), in the crystal structure of electride Rb+ (C222)e− . Connection along b (near perpendicular to the plane of the figure) between chains involves channel C (not labeled). The c axis is in the plane at 72◦ to the horizontal.

N

N

B

N N

N

B

S

S A

N

A S

B

m

0p

70

A 873 pm

A

Fig. 12.4.3.

S A

S

B

tripiperazine cryptand TripPip222 (a)

(b)

Figure 12.4.3(b) displays the cavity-channel geometry in the crystal structure of Rb+ (C222)e− , in which the dominant void space consists of parallel zigzag chains of cavities S and large channels A (diameter 260 pm) along the a-direction, which are connected at the “corners” by narrower channel B of diameter 115 pm to form “ladder-like” one-dimensional chains along a. Adjacent chains are connected along b by channels C of diameter 104 pm and along c by channels with diameter of 72 pm. Thus the void space in the crystal comprises a three-dimensional network of cavities and channels. The inter-electron coupling in adjacent cavities depends on the extent of overlap of the electronic wavefunction. The dimensionalities, diameters, and lengths of the channels that

Alkali and Alkaline-Earth Metals connect the cavities play major roles. These structural features are consistent with the nature of wave–particle duality of the electron. Removal of enclathrated oxygen ions from the cavities in a single crystal of 12CaO·7Al2 O3 leads to the formation of the thermally and chemically stable electride [Ca24Al28 O64 ]4+ (e− )4 . 12.5

Survey of the alkaline-earth metals

Beryllium, magnesium, calcium, strontium, barium, and radium constitute Group 2 in the Periodic Table. These elements (or simply the Ca, Sr, and Ba triad) are often called alkaline-earth metals. Some important properties of group 2 elements are summarized in Table 12.5.1. All group 2 elements are metals, but an abrupt change in properties between Be and Mg occurs as Be shows anomalous behavior in forming mainly covalent compounds. Beryllium most frequently displays a coordination number of four, usually tetrahedral, in which the radius of Be2+ is 27 pm. The chemical behavior of magnesium is intermediate between that of Be and the heavier elements, and it also has some tendency for covalent bond formation. With increasing atomic number, the group 2 metals follow a general trend in decreasing values of I1 and I2 except for Ra, whose relatively high I1 and I2 are attributable to the 6s inert pair effect. Also, high I3 values for all members of the group preclude the formation of the +3 oxidation state. As the atomic number increases, the electronegativity decreases. In the organic compounds of group 2 elements, the polarity of the M–C bond increases in the order BeR 2 < MgR 2 < CaR 2 < SrR 2 < BaR 2 < RaR 2 This is due to the increasing difference between the χs of carbon (2.54) and those of the metals. The tendency of these compounds to aggregate also increases in the same order. The BeR2 and MgR2 compounds are linked in the solid phase Table 12.5.1. Properties of group 2 elements

Property Atomic number, Z Electronic configuration 'Hat0 (kJ mol−1 ) mp (K) 'Hfuse (mp) (kJ mol−1 ) bp (K) rM (CN = 12) (pm) rM2+ (CN = 6) (pm) I1 (kJ mol−1 ) I2 (kJ mol−1 ) I3 (kJ mol−1 ) χs mp of MCl2 (K)

Be

Mg

Ca

Sr

Ba

Ra

4 [He]2s2 309 1551 7.9 3243 112 45 899.5 1757 14850 1.58 703

12 [Ne]3s2 129 922 8.5 1363 160 72 737.3 1451 7733 1.29 981

20 [Ar]4s2 150 1112 8.5 1757 197 100 589.8 1145 4912 1.03 1045

38 [Kr]5s2 139 1042 7.4 1657 215 118 549.5 1064 4138 0.96 1146

56 [Xe]6s2 151 1002 7.1 1910 224 135 502.8 965.2 3619 0.88 1236

88 [Rn]7s2 130 973 — 1413 — 148 509.3 979.0 3300 — —

449

450

Structural Chemistry of Selected Elements via M–C–M 3c-2e covalent bonds to form polymeric chains, while CaR2 to RaR2 form three-dimensional network structures in which the M–C bonds are largely ionic. All the M2+ ions are smaller and considerably less polarizable than the isoelectronic M+ ions, as the higher effective nuclear charge binds the remaining electrons tightly. Thus the effect of polarization of cations on the properties of their salts are less important. Ca, Sr, Ba, and Ra form a closely allied series in which the properties of the elements and their compounds vary systematically with increasing size in much the same manner as in the alkali metals. The melting points of group 2 metal chlorides MCl2 increase steadily, and this trend is in sharp contrast to the alkali metal chlorides: LiCl (883 K), NaCl (1074 K), KCl (1045 K), RbCl (990 K), and CsCl (918 K). This is due to several subtle factors: (a) the nature of bonding varies from covalent (Be) to ionic (Ba); (b) from Be to Ra the coordination number increases, so the Madelung constants, the lattice energies, and the melting points also increase; (c) the radius of Cl− is large (181 pm), whereas the radii of M2+ are small, and in the case of metal coordination, an increase in the radius of M2+ reduces the Cl− · · · Cl− repulsion. 12.6

Structure of compounds of alkaline-earth metals

12.6.1

Group 2 metal complexes

The coordination compounds of the alkaline-earth metals are becoming increasingly important to many branches of chemistry and biology. A considerable degree of structural diversity exists in these compounds, and monomers up to nonametallic clusters and polymeric species are known. Beryllium, in view of its small size and simple set of valence orbitals, almost invariably exhibits tetrahedral four-coordination in its compounds. Figure 12.6.1(a) shows the structure of Be4 O(NO3 )6 . The central oxygen atom is tetrahedrally surrounded by four Be atoms, and each Be atom is in turn tetrahedrally surrounded by four O atoms. The six nitrate groups are attached symmetrically to the six edges of the tetrahedron. This type of structure also appears in Be4 O(CH3 COO)6 . Magnesium shows a great tendency to form complexes with ligands which have oxygen and nitrogen donor atoms, often displaying six-coordination, and its compounds are more polar than those of beryllium. The structure of hexameric [MgPSit Bu3 ]6 is based on a Mg6 P6 hexagonal drum, with Mg–P distances varying between 247 and 251 pm in the six-membered Mg3 P3 ring, and 250 and 260 pm between the two rings, as shown in Fig. 12.6.1(b). Calcium, strontium, and barium form compounds of increasing ionic character with higher coordination numbers, of which six to eight are particularly common. The complex Ca9 (OCH2 CH2 OMe)18 (HOCH2 CH2 OMe)2 has an interesting structure: the central Ca9 (µ3 -O)8 (µ2 -O)8 O20 skeleton is composed of three six-coordinate Ca atoms and six seven-coordinate Ca atoms that can be viewed as filling the octahedral holes in two close-packed oxygen layers, as shown in Fig. 12.6.1(c). The distances of Ca–O are Ca–(µ3 -O) 239 pm, Ca–(µ2 -O) 229 pm and Ca–Oether 260 pm.

Alkali and Alkaline-Earth Metals (a)

451

(b)

P Be

Mg O SiBu3

N

(c)

(d)

O Ca O

Ba I THF

Fig. 12.6.1.

Structures of some coordination compounds of alkaline-earth metals: (a) Be4 O(NO3 )6 , (b) [MgPSit Bu3 ]6 , (c) Ca9 (OCH2 CH2 OMe)18 (HOCH2 CH2 OMe)2 and (d) [BaI(BHT)(THF)3 ]2 .

In the dimeric complex [BaI(BHT)(THF)3 ]2 [BHT = 2,6-di-t-butyl-4methylphenol, C6 H2 Met Bu2 (OH)], the coordination geometry around the Ba atom is distorted octahedral, with the two bridging iodides, the BHT, and a THF ligand in one plane, and two additional THF molecules lying above and below the plane, as shown in Fig. 12.6.1(d). The bond distances are Ba–I 344 pm, Ba–OAr 241 pm (av). Many interesting coordination compounds of Group 2 elements have been synthesized in recent years. For example, the cation [Ba(NH3 )n ]2+ is generated in the course of reducing the fullerenes C60 and C70 with barium in liquid ammonia. In the [Ba(NH3 )7 ]C60 ·NH3 crystal, the Ba2+ cation is surrounded by seven NH3 ligands at the vertices of a monocapped trigonal antiprism, and the C60 dianion is well ordered. In the [Ba(NH3 )9 ]C70 ·7NH3 crystal, the coordination geometry around Ba2+ is a distorted tricapped trigonal prism, with Ba–N distances in the range 289–297 pm; the fullerene C70 units are linked into slightly zigzag linear chains by single C–C bonds with length 153 pm. 12.6.2

Group 2 metal nitrides

The crystals of M[Be2 N2 ] (M = Mg, Ca, Sr) are composed of complex anion layers with covalent bonds between Be and N atoms. For example, Mg[Be2 N2 ] contains puckered six-membered rings in the chair conformation. These rings are condensed into single nets and are further connected to form double layers,

C

452

Structural Chemistry of Selected Elements

Fig. 12.6.2.

Crystal structures of (a) Mg[Be2 N2 ] and (b) Ca[Be2 N2 ]. Small circles represent Be, large circles N, while circles between layers are either Mg or Ca.

(a)

(b)

in which the Be and N atoms are alternately linked. In this way, each beryllium atom is tetrahedrally coordinated by nitrogens, while each nitrogen occupies the apex of a trigonal pyramid whose base is made of three Be atoms, and a fourth Be atom is placed below the base. Thus the nitrogen atoms are each coordinated by an inverse tetrahedron of Be atoms and occupy positions at the outer boundaries of a double layer, as shown in Fig. 12.6.2(a). The Be– N bond lengths are 178.4 pm (3×) and 176.0 pm. The magnesium atoms are located between the anionic double layers, and each metal center is octahedrally surrounded by nitrogens with Mg–N 220.9 pm. The ternary nitrides Ca[Be2 N2 ] and Sr[Be2 N2 ] are isostructural. The crystal structure contains planar layers which consist of four- and eight-membered rings in the ratio of 1:2. The layers are stacked with successive slight rotation of each about the common normal, forming octagonal prismatic voids in the interlayer region. The eight-coordinated Ca2+ ions are accommodated in the void space, as shown in Fig. 12.6.2(b). The Be–N bond lengths within the layers are 163.2 pm (2×) and 165.7 pm. The Ca–N distance is 268.9 pm. 12.6.3

Group 2 low-valent oxides and nitrides

(1) (Ba2 O)Na Similar to the alkali metals, the alkaline-earth metals can also form low-valent oxides. The first crystalline compound of this type is (Ba2 O)Na, which belongs to space group Cmma with a = 659.1, b = 1532.7, c = 693.9 pm, and Z = 4. In the crystal structure, the O atom is located inside a Ba4 tetrahedron. Such [Ba4 O] units share trans edges to form an infinite chain running parallel to the a axis. The [Ba4/2 O]∞ chains are in parallel alignment and separated by the Na atoms, as illustrated in Fig. 12.6.3. Within each chain, the Ba–O bond length is 252 pm, being shorter than the corresponding distance of 277 pm in crystalline barium oxide. The interatomic distances between Ba and Na atoms lie in the range 421–433 pm, which are comparable with the values in the binary alloys BaNa and BaNa2 (427 and 432 pm, respectively). (2) [Ba6 N] cluster and related compounds When metallic barium is dissolved in liquid sodium or K/Na alloy in an inert atmosphere of nitrogen, an extensive class of mixed alkali metal–barium

Alkali and Alkaline-Earth Metals

453

b c

Fig. 12.6.3.

Crystal structure of (Ba2 O)Na. The [Ba4/2 O]∞ chains are seen end-on.

subnitrides can be prepared. They contain [Ba6 N] octahedra that exist either as discrete entities or are condensed into finite clusters and infinite arrays. Discrete [Ba6 N] clusters are found in the crystal structure of (Ba6 N)Na16 , ¯ with as shown in Fig. 12.6.4. (Ba6 N)Na16 crystallizes in space group Im3m a = 1252.7 pm and Z = 2. The Na atoms are located between the cluster units, in a manner analogous to that in the low-valent alkali metal suboxides. The series of barium subnitrides Ba3 N, (Ba3 N)Na, and (Ba3 N)Na5 are characterized by parallel infinite (Ba6/2 N)∞ chains each composed of trans face-sharing octahedral [Ba6 N] clusters. Figure 12.6.5(a) shows the crystal structure of Ba3 N projected along a sixfold axis. In the crystal structure of (Ba3 N)Na, the sodium atoms are located in between the (Ba6/2 N)∞ chains, as shown in Fig. 12.6.5(b). In contrast, since (Ba3 N)Na5 has a much higher sodium content, the (Ba6/2 N)∞ chains are widely separated from one another by the additional Na atoms, as illustrated in Fig. 12.6.5(c).

Fig. 12.6.4.

Arrangement of the (Ba6 N) clusters in the crystal structure of (Ba6 N)Na16 .

(3) [Ba14 CaN6 ] cluster and related compounds The [Ba14 CaN6 ] cluster can be considered as a Ca-centered Ba8 cube with each face capped by a Ba atom, and the six N atoms are each located inside a Ba5 tetragonal pyramid, as shown in Fig. 12.6.6. The structure can be viewed alternatively as a cluster composed of the fusion of six N-centered Ba5 Ca octahedra sharing a common Ca vertex. In the synthesis of this type of cluster compounds, variation of the atomic ratio of the Na/K binary alloy system leads to a series of compounds of variable stoichiometry: [Ba14 CaN6 ]Nax with x = 7, 8, 14, 17, 21

454

Structural Chemistry of Selected Elements (a)

(c)

(b)

Fig. 12.6.5.

Crystal structures of (a) Ba3 N, (b) (Ba3 N)Na and (c) (Ba3 N)Na5 . The (Ba6/2 N)∞ chains are seen end-on.

and 22. This class of compounds can be considered as composed of an ionically 2+ 3− bonded [Ba2+ 8 Ca N6 ] nucleus surrounded by Ba6 Nax units, which interact with the nucleus mainly via metallic bonding.

12.7

Organometallic compounds of group 2 elements

There are numerous organometallic compounds of Group 2 elements, and in this section only the following three typical species are described. 12.7.1 Fig. 12.6.6.

Structure of the [Ba14 CaN6 ] cluster.

Polymeric chains

Dimethylberyllium, Be(CH3 )2 , is a polymeric white solid containing infinite chains, as shown in Fig. 12.7.1(a). Each Be center is tetrahedrally coordinated and can be considered to be sp3 hybridized. As the CH3 group only contributes one orbital and one electron to the bonding, there are insufficient electrons to form normal 2c-2e bonds between the Be and C atoms. In this electron-deficient system, the BeCBe bridges are 3c-2e bonds involving sp3 hybrid atomic orbitals from two Be atoms and one C atom, as shown in Fig. 12.7.1(b). The polymeric structures of BeH2 and BeCl2 are similar to that of Be(CH3 )2 . The 3c-2e bonding in BeH2 is analogous to that in Be(CH3 )2 . But in BeCl2 there are sufficient valence electrons to form normal 2c-2e Be–Cl bonds. 12.7.2

Grignard reagents

Grignard reagents are widely used in organic chemistry. They are prepared by the interaction of magnesium with an organic halide in ethers. Grignard reagents

Alkali and Alkaline-Earth Metals

455

+ +

+

+

+ + Fig. 12.7.1.

(a)

(b)

(a) Linear structure of Be(CH3 )2 ; (b) its BeCBe 3c-2e bonding in the polymer.

Br O

C

Mg

Fig. 12.7.2.

Molecular structure of Grignard reagent (C2 H5 )MgBr·2(C2 H5 )2 O.

are normally assigned the simple formula RMgX, but this is an oversimplification as solvation is important. The isolation and structural determination of several crystalline RMgX compounds have demonstrated that the essential structure is RMgX·(solvent)n . Figure 12.7.2 shows the molecular structure of (C2 H5 )MgBr·2(C2 H5 )2 O, in which the central Mg atom is surrounded by one ethyl group, one bromine atom, and two diethyl ether molecules in a distorted tetrahedral configuration. The bond distances are Mg–C 215 pm, Mg–Br 248 pm, and Mg–O 204 pm. The latter is among the shortest Mg–O distances known. In a Grignard compound the carbon atom bonded to the electropositive Mg atom carries a partial negative charge. Consequently a Grignard reagent is an extremely strong base, with its carbanion-like alkyl or aryl portion acting as a nucleophile. 12.7.3

Alkaline-earth metallocenes

The alkaline-earth metallocenes exhibit various structures, depending on the sizes of the metal atoms. In Cp2 Be, the Be2+ ion is η5 /η1 coordinated between two Cp rings, as shown in Fig. 12.7.3(a). The mean Be–C distances are 193 and 183 pm for η5 and η1 Cp rings, respectively. In contrast, Cp2 Mg adopts a typical sandwich structure, as shown in Fig. 12.7.3(b). The mean Mg–C distance is 230 pm. In the crystalline state, the two parallel rings have a staggered conformation. The compounds Cp2 Ca, Cp∗ Sr and Cp∗ Ba exhibit a different coordination mode, as the two Cp rings are not aligned in a parallel fashion like Cp2 Mg, but

456

Structural Chemistry of Selected Elements (a)

(b) (e) Mg

Be

Ba (c)

Fig. 12.7.3.

(d)

Ca

Structures of some alkaline-earth metallocenes: (a) Cp2 Be, (b) Cp2 Mg, (c) Cp2 Ca, (d) Sr[C5 H3 (SiMe3 )2 ]2 ·THF, (e) Ba2 (COT) [C5 H(CHMe2 )4 ]2 .

Sr

are bent with respect to each other making a Cp(centroid) –M–Cp(centroid) angle of 147◦ –154◦ . The positive charge of the M2+ ion is not only shared by two η5 -bound Cp rings, but also by other ligands. In Cp2 Ca, apart from the two η5 -Cp ligands, there are significant Ca–C contacts to η3 - and η1 -Cp rings, as shown in Figure 12.7.3(c). In Sr[C5 H3 (SiMe3 )2 ]2 ·THF, apart from the two η5 -Cp rings, a THF ligand is coordinated to the Sr2+ ion , as shown in Fig. 12.7.3(d). The Ba2+ ion has the largest size among the alkaline-earth metals, and accordingly it can be coordinated by a planar COT (C8 H8 ) ring bearing two negative charges. Figure 12.7.3(e) shows the structure of a triple-decker sandwich complex of barium, Ba2 (COT)[C5 H(CHMe2 )4 ]2 , in which the mean Ba–C distances are 296 and 300 pm for the η5 -Cp ring and η8 -COT ring, respectively.

12.8

Alkali and alkaline-earth metal complexes with inverse crown structures

The term “inverse crown ether” refers to a metal complex in which the roles of the central metal core and the surrounding ether oxygen ligand sites in a conventional crown ether complex are reversed. An example of an inverse crown ether is the organosodium-zinc complex Na2 Zn2 {N(SiMe3 )2 }4 (O) shown in Fig. 12.8.1(a). The general term “inverse crown” is used when the central core of this type of complex comprises non-oxygen atoms, or more than just a single O atom. Two related inverse crowns with cationic (Na–N–Mg–N–)2 rings that encapsulate peroxide and alkoxide groups, respectively, are shown in Figs. 12.8.1(b) and (c). The octagonal macrocycle in Na2 Mg2 {N(SiMe3 )2 }4 (OOctn )2 takes the chair form with the Na–OOctn groups displaced on either side of the plane defined by the N and Mg atoms. Each alkoxide O atom interacts with both Mg atoms to produce a perfectly planar

Alkali and Alkaline-Earth Metals (a)

(b)

R R N

R

R

Na

Zn

O

N

Na

N

R

R R

R

N R

R

R = SiMe3

Na

N Mg

Zn

R

(c)

O

N

R

N

R R

O Mg N

Na

(d)

R R

N Mg

R R

R = SiMe3

R R

457

N

Na O

N

R'

R' O Na

R R

Na N

Mg N

R R

R = Pri; R' = Octn

Na

N

Na O Mg O

Mg

Mg O N Mg N

O

N O

Na

Mg O

Mg Na

N

Na

Fig. 12.8.1.

Examples of some inverse crown compounds: (a) Na2 Zn2 {N(SiMe3 )2 }4 (O), (b) Na2 Mg2 {N(SiMe3 )2 }4 (O2 ), (c) Na2 Mg2 {N(SiMe3 )2 }4 (OOctn )2 , (d) cluster core of {(THF)NaMg(Pri2 N)(O)}6 ; the THF ligand attached to each Na atom and the isopropyl groups are omitted for clarity.

(MgO)2 ring. The Mg–O and Na–Osyn bond lengths are 202.7(2)-203.0(2) and 256.6(1)-247.2(2) pm, respectively; the non-bonded Na· · · Oanti distances lie in the range 310.4(1)-320.4(2) pm. Figure 12.8.1(d) shows the structure of a hexameric “super” inverse crown ether {(THF)NaMg(Pri2 N)(O)}6 , which consists of a S6 -symmetric hexagonal prismatic Mg6 O6 cluster with six external four-membered rings constructed with Na–THF and Pri2 N appendages. Table 12.8.1. Compositions of some inverse crowns containing organic guest

species Group 1 metal

Group 2 metal

Amide ion

Core moiety

Host ring size

4Na 4Na 6K 6K 4Na

2Mg 2Mg 6Mg 6Mg 4Mg

6TMP 6TMP 12TMP 12TMP 8Pri2 N

C6 H3 Me2− C6 H2− 4 6C6 H− 5 6C6 H4 Me− Fe(C5 H3 )4− 2

12 12 [Fig. 2.7.5(a)] 24 24 12 [Fig. 2.7.5(b)]

A remarkable series of inverse crown compounds featuring organic guest moieties encapsulated within host-like macrocyclic rings composed of sodium/potassium and magnesium ions together with anionic amide groups, such as TMP− (TMPH = 2,2,6,6-tetramethylpiperidine) and Pri2 N− (Pri2 NH = diisopropylamine), have been synthesized and characterized. Table 12.8.1 lists some examples of this class of inverse crown molecules. Figure 12.8.2(a) shows the molecular structure of Na4 Mg2 (TMP)6 (C6 H4 ), in which the N atom of each tetramethylpiperidinide is bonded to two metal atoms to form a cationic 12-membered (Na–N–Na–N–Mg–N–)2 ring. The mixed metal macrocyclic amide acts as a host that completely encloses a 1,4deprotonated benzenediide guest species whose naked carbon atoms are each stabilized by a covalent Mg–C bond and a pair of Na· · · C π interactions.

458

Structural Chemistry of Selected Elements (a)

(b)

Fe

Mg Na

N

Fig. 12.8.2.

Molecular structures of two centrosymmetric inverse crown molecules containing organic cores: (a) Na4 Mg2 (TMP)6 (C6 H4 ), (b) Na4 Mg4 (i Pr2 N)8 [Fe(C5 H3 )2 ]. The Na· · ·C π interactions are indicated by broken lines.

Figure 12.8.2(b) shows the molecular structure of Na4 Mg4 (Pri2 N)8 [Fe(C5 H3 )2 ]. Each amido N atom is bound to one Na and one Mg atom to form a 16-membered macrocyclic ring, which accommodates the ferrocene1,1’,3,3’-tetrayl residue at its center. The deprotonated 1,3-positions of each cyclopentadienyl ring of the ferrocene moiety are each bound to a pair of Mg atoms by Mg–C covalent bonds, and the 1,2,3-positions further interact with three Na atoms via three different kinds of Na· · · C π bonds. References 1. N. Wiberg, Inorganic Chemistry, 1st English edn. (based on Holleman-Wiberg: Lehrbuch der Anorganischen Chemie, 34th edn., Walter de Gruyter, Berlin, 1995), Academic Press, San Diego, CA, 2001. 2. F. A. Cotton, G. Wilkinson, C. A. Murillo and M. Bochmann, Advanced Inorganic Chemistry, 6th edn., Wiley-Interscience, New York, 1999. 3. A. G. Massey, Main Group Chemistry, 2nd edn., Wiley, Chichester, 2000. 4. C. E. Housecroft and A. G. Sharpe, Inorganic Chemistry, 2nd edn., Prentice-Hall, Harlow, 2004. 5. D. F. Shriver, P. W. Atkins, T. L. Overton, J. P. Rourke, M. T. Weller and F. A. Armstrong, Inorganic Chemistry, 4th edn., Oxford University Press, Oxford, 2006. 6. A.-M. Sapse and P. von R. Schleyer, Lithium Chemistry: A Theoretical and Experimental Overview, Wiley, NewYork, 1995. 7. T. C. W. Mak and G.-D. Zhou, Crystallography in Modern Chemistry: A Resource Book of Crystal Structures, Wiley, New York, 1992. 8. M. Gielen, R. Willen, and B. Wrackmeyer (eds.), Unusual Structures and Physical Properties in Organometallic Chemistry, Wiley, West Sussex, 2002. 9. J. A. McCleverty and T. J. Meyer (editors-in-chief), Comprehensive Coordination Chemistry: From Biology to Nanotechnology, vol. 3, G. F. R. Parkin (volume ed.),

Alkali and Alkaline-Earth Metals

10.

11.

12. 13.

14. 15. 16.

17.

18.

19. 20.

21.

Coordination Chemistry of the s, p, and f Metals, Elsevier-Pergamon, Amsterdam, 2004. A. Simon, Alkali and alkaline earth metal suboxides and subnitrides. In M. Driess and H. Nöth (eds.), Molecular Clusters of the Main Group Elements, Wiley–VCH, Weinheim, 2004, pp. 246–66. M. Driess, R. E. Mulvey and M. Westerhausen, Cluster growing through ionic aggregation: synthesis and structural principles of main group metal-nitrogen, phosphorus and arsenic rich clusters. In M. Driess and H. Nöth (eds.), Molecular Clusters of the Main Group Elements, Wiley–VCH, Weinheim, 2004, pp. 246–66. J. L. Dye, Electrides: From LD Heisenberg chains to 2D pseudo-metals. Inorg. Chem. 36, 3816–26 (1997). Q. Xie, R. H. Huang, A. S. Ichimura, R. C. Phillips, W. P. Pratt Jr. and J. L. Dye, Structure and properties of a new electride, Rb+ (cryptand[2.2.2])e− . J. Am. Chem. Soc. 122, 6971–8 (2000). M. Y. Redko, J. E. Jackson, R. H. Huang and J. L. Dye, Design and synthesis of a thermally stable organic electride. J. Am. Chem. Soc. 127, 12416–22 (2005). H. Sitzmann, M. D. Walter and G. Wolmershäuser, A triple-decker sandwich complex of barium. Angew. Chem. Int. Ed. 41, 2315–16 (2002). S. Matsuishi, Y. Toda, M. Miyakawa, K. Hayashi, T. Kamiya, M. Hirano, I. Tanaka and H. Hosono, High-density electron anions in a nanoporous single crystal: [Ca24Al28 O64 ]4+ (4e− ). Science 301, 626–9 (2003). M. Sebastian, M. Nieger, D. Szieberth, L. Nyulaszi and E. Niecke, Synthesis and structure of a 1,3-diphospha-cyclobutadienediide. Angew. Chem. Int. Ed. 43, 637–41 (2004). D. Stalke, The lithocene anion and “open” calcocene — new impulses in the chemistry of alkali and alkaline earth metallocenes. Angew. Chem. Int. Ed. 33, 2168–71(1994). J. Geier and H. Grützmacher, Synthesis and structure of [Na11 (Ot Bu)10 (OH)]. Chem. Commun. 2942–3 (2003). M. Somer, A. Yarasik, L. Akselrud, S. Leoni, H. Rosner, W. Schnelle and R. Kniep, Ae[Be2 N2 ]: Nitridoberyllates of the heavier alkaline-earth metals. Angew. Chem. Int. Ed. 43, 1088–92 (2004). R. E. Mulvey, s-Block metal inverse crowns: synthetic and structural synergism in mixed alkali metal-magnesium (or zinc) amide chemistry. Chem. Commun. 1049–56 (2001).

459

13

Structural Chemistry of Group 13 Elements

13.1

Survey of the group 13 elements

Boron, aluminum, gallium, indium, and thallium are members of group 13 of the Periodic Table. Some important properties of these elements are given in Table 13.1.1. From Table 13.1.1, it is seen that the inner electronic configurations of the group 13 elements are not identical. The ns2 np1 electrons of B and Al lie outside a rare gas configuration, while the ns2 np1 electrons of Ga and In are outside the d 10 subshell, and those of Tl lie outside the 4f 14 5d 10 core. The increasing effective nuclear charge and size contraction, which occur during successive filling of d and f orbitals, combine to make the outer s and p electrons of Ga, In, and Tl more strongly held than expected by simple extrapolation from B to Al. Thus there is a small increase in ionization energy between Al and Ga, and between In and Tl. The drop in ionization energy between Ga and In mainly

Table 13.1.1. Table 13.1.1 Some properties of group 13 elements

Property Atomic number, Z Electronic configuration 'Hatθ (kJ mol−1 ) mp (K) θ (kJ mol−1 ) 'Hfuse bp (K) I1 (kJ mol−1 ) I2 (kJ mol−1 ) I3 (kJ mol−1 ) I1 + I2 + I3 (kJ mol−1 ) χs rM (pm) rcov (pm) rion, M3+ (pm) rion, M+ (pm) D0, M–F (in MF3 ) (kJ mol−1 ) D0, M–Cl (in MCl3 ) (kJ mol−1 ) ∗

For β-rhombohedral boron

B

Al

Ga

In

Tl

5 [He]2s2 2p1 582 2453∗ 50.2 4273 800.6 2427 3660 6888 2.05 — 88 — — 613 456

13 [Ne]3s2 3p1 330 933 10.7 2792 577.5 1817 2745 5140 1.61 143 130 54 — 583 421

31 [Ar]3d 10 4s2 4p1 277 303 5.6 2477 578.8 1979 2963 5521 1.76 153 122 62 113 469 354

49 [Kr]4d 10 5s2 5p1 243 430 3.3 2355 558.3 1821 2704 5083 1.66 167 150 80 132 444 328

81 [Xe]4f 14 5d 10 6s2 6p1 182 577 4.1 1730 589.4 1971 2878 5438 1.79 171 155 89 140 439 (in TlF) 364 (in TlCl)

Group 13 Elements reflects the fact that both elements have a completely filled inner shell and the outer electrons of In are further from the nucleus. The +3 oxidation state is characteristic of group 13 elements. However, as in the later elements of this groups, the trend in I2 and I3 shows increases at Ga and Tl, leading to a marked increase in stability of their +1 oxidation state. In the case of Tl, this is termed the 6s inert-pair effect. Similar effects are observed for Pb (group 14) and Bi (group 15), for which the most stable oxidation states are +2 and +3, respectively, rather than +4 and +5. Because of the 6s inert-pair effect, many Tl+ compounds are found to be more stable than the corresponding Tl3+ compounds. The progressive weakening of M3+ –X bonds from B to Tl partly accounts for this. Furthermore, the relativistic effect (as described in Section 2.4.3) is another factor which contributes to the inert-pair effect.

13.2

Elemental Boron

The uniqueness of structure and properties of boron is a consequence of its electronic configuration. The small number of valence electrons (three) available for covalent bond formation leads to “electron deficiency,” which has a dominant effect on boron chemistry. Boron is notable for the complexity of its elemental crystalline forms. There are many reported allotropes, but most are actually boron-rich borides. Only two have been completely elucidated by X-ray diffraction, namely α-R12 and β-R105; here R indicates the rhombohedral system, and the numeral gives the number of atoms in the primitive unit cell. In addition, α-T50 boron (T denotes the tetragonal system) has been reformulated as a carbide or nitride, B50 C2 or B50 N2 , and β-T192 boron is still not completely elucidated. These structures all contain icosahedral B12 units, which in most cases are accompanied by other boron atoms lying outside the icosahedral cages, and the linkage generates a three-dimensional framework. The α-R12 allotrope consists of an approximately cubic closest packing arrangement of icosahedral B12 units bound to each other by covalent bonds. The parameters of the rhombohedral unit cell are a = 505.7 pm, α = 58.06◦ ¯ the unit cell contains one B12 icosahe(60◦ for regular ccp). In space group R3m, dron. A layer of interlinked icosahedra perpendicular to the threefold symmetry axis is illustrated in Fig. 13.2.1. There are 12 neighboring icosahedra for each icosahedron: six in the same layer, and three others in each of the upper and lower layers, as shown in Fig. 9.6.21(b). The B12 icosahedron is a regular polyhedron with 12 vertices, 30 edges, and 20 equilateral triangular faces, with B atoms located at the vertices, as shown in Fig. 13.2.2. The B12 icosahedron is a basic structural unit in all isomorphic forms of boron and in some polyhedral boranes such as B12 H2− 12 . It has 36 valence electrons; note that each line joining two B atoms (mean B–B distance 177 pm) in Fig. 13.2.2 does not represent a normal two-center two-electron (2c-2e) covalent bond. When the total number of valence electrons in a molecular skeleton is less than the number of valence orbitals, the formation of normal 2c-2e covalent

461

462

Structural Chemistry of Selected Elements

Fig. 13.2.1.

A close-packed layer of interlinked icosahedra in the crystal structure of α-rhomobohedral boron. The lines meeting at a node (not a B atom) represents a BBB 3c-2e bond linking three B12 icosahedra.

bonds is not feasible. In this type of electron-deficient compound, three-center two-electron (3c-2e) bonds generally occur, in which three atoms share an electron pair. Thus one 3c-2e bond serves to compensate for the shortfall of four electrons and corresponds to a bond valence value of 2, as illustrated for a BBB bond in Fig. 13.2.3. (a)

(b)

(c)

Fig. 13.2.2.

From left to right, perspective view of the B12 icosahedron along one of its (a) 6 fivefold, (b) 10 threefold, and (c) 15 twofold axes.

In a closo-Bn skeleton, there are only three 2c-2e covalent bonds and (n − 2) BBB 3c-2e bonds. (This will be derived in Section 13.4.) For an icosahedral B12 unit, there are three B–B 2c-2e bonds and ten BBB 3c-2e bonds, as shown in Fig. 13.2.4. (a)

(b)

–

B

+ Fig. 13.2.3.

The BBB 3c-2e bond: (a) three atoms share an electron pair, and (b) simplified representation of 3c-2e bond.

+ –

+ –

B

B

The 36 electrons in the B12 unit may be partitioned as follow: 26 electrons are used to form bonds within an icosahedron, and the remaining ten

Group 13 Elements 1

1

2

6

3

6

9

Fig. 13.2.4.

11 5

12 3

5 4

4

(a)

2

10

8

7

463

Chemical bonds in the B12 icosahedron (one of many possible canonical forms): three 2c-2e bonds between 1–10, 3–12, and 5–11; ten BBB 3c-2e bonds between 1–2–7, 2–3–7, 3–4–9, . . ..

(b)

Fig. 13.2.5.

Structure of β-R105 boron: (a) perspective view of the B84 unit [B12a @B12 @B60 ]. Black circles represent the central B12a icosahedron, shaded circles represent the B atoms connecting the surface 60 B atoms to the central B12a unit; (b) each vertex of inner B12a is connected to a pentagonal pyramidal B6 unit (only two adjoining B6 units are shown).

electrons to form the intericosahedral bonds. In the structure of α-R12 boron, each icosahedron is surrounded by six icosahedra in the same layer and forms six 3c-2e bonds [see Fig. 9.6.21(b)], in which every B atom contributes 2/3 electron, so each icosahedron uses 6 × 2/3 = 4 electrons. Each icosahedron is bonded by normal 2c-2e B–B bonds to six icosahedra in the upper and lower layers, which need six electrons. The number of bonding electrons in an icosahedron of α-R12 boron is therefore 26 + 4 + 6 = 36. The β-R105 boron allotrope has a much more complex structure with 105 ¯ a = 1014.5 pm, α = 65.28◦ ). A B atoms in the unit cell (space group R3m, basic building unit in the crystal structure is the B84 cluster illustrated in Fig. 13.2.5(a); it can be considered as a central B12a icosahedron linked radially to 12 B6 half-icosahedra (or pentagonal pyramids), each attached like an inverted umbrella to an icosahedral vertex, as shown in Fig. 13.2.5(b). The basal B atoms of adjacent pentagonal pyramids are interconnected to form a B60 icosahedron that resembles fullerene-C60 . The large B60 icosahedron encloses the B12a icosahedron, and the resulting B84 cluster can be formulated as B12a @B12 @B60 . Additionally, a six-coordinate B atom lies at the center of symmetry between two adjacent B10 condensed units, and the crystal structure is an intricate coordination network resulting from the linkage of B10 –B–B10 units and B84 clusters, such that all 105 atoms in the unit cell except one are the vertices of fused icosahedra. Further details and the electronic structure of β-R105 boron are described in Section 13.4.6.

464

Structural Chemistry of Selected Elements 13.3

Borides

Solid borides have high melting points, exceptionally high hardness, excellent wear resistance, and good immunity to chemical attack, which make them industrially important with uses as refractory materials and in rocket cones and turbine blades. Some metal borides have been found to exhibit superconductivity. 13.3.1

Metal borides

A large number of metal borides have been prepared and characterized. Several hundred binary metal borides Mx By are known. With increasing boron content, the number of B–B bonds increases. In this manner, isolated B atoms, B–B pairs, fragments of boron chains, single chains, double chains, branched chains, and hexagonal networks are formed, as illustrated in Fig. 13.3.1. Table 13.3.1 summarizes the stoichiometric formulas and structures of metal borides. In boron-rich compounds, the structure can often be described in terms of a three-dimensional network of boron clusters (octahedra, icosahedra, and cubooctahedra), which are linked to one another directly or via non-cluster atoms. (a)

(b)

(c)

(d)

(e)

(f)

Fig. 13.3.1.

Idealized patterns of boron catenation in metal-rich borides: (a) isolated boron atoms, (b) B–B pairs, (c) single chain, (d) branched chain, (e) double chain, (f) hexagonal net in MB2 . Table 13.3.1. Stoichiometric formulas and structure of metal borides

Formula

Example

M4 B M3 B M5 B2 M7 B3 M2 B M3 B2 MB M11 B8 M3 B4 MB2 MB4 MB6 MB12 MB15 MB66

Mn4 B, Cr4 B Ni3 B, Co3 B Pd5 B2 Ru7 B3 , Re7 B3 Be2 B, Ta2 B V3 B2 , Nb3 B2 FeB, CoB Ru11 B8 Ta3 B4 , Cr3 B4 MgB2 , AlB2 LaB4 , ThB4 CaB6 YB12 , ZrB12 NaB15 YB66

Catenation of boron and figure showing structure

  

isolated B atom, Fig. 13.3.1(a)

B2 pairs, Fig. 13.3.1(b) single chains, Fig. 13.3.1(c) branched chains, Fig. 13.3.1(d) double chains, Fig. 13.3.1(e) hexagonal net, Fig. 13.3.1(f) and Fig. 13.3.2 B6 octahedra and B2 Fig. 13.3.3(a) B6 octahedra, Fig. 13.3.3(b) B12 cubooctahedra, Fig. 13.3.4(a) B12 icosahedra, Fig. 13.3.4(b) and B3 unit B12 ⊂ (B12 )12 giant cluster

Group 13 Elements

465

Fig. 13.3.2.

Crystal structure of MgB2 .

The metal atoms are accommodated in cages between the octahedra or icosahedra, thereby providing external bonding electrons to the electron-deficient boron network. The structures of some metal borides in Table 13.3.1 are discussed below. (1) MgB2 and AlB2 Magnesium boride MgB2 was discovered in 2001 to behave as a superconductor at Tc = 39 K, and its physical properties are similar to those of Nb3 Sn used in the construction of high-field superconducting magnets in NMR spectrometers. MgB2 crystallizes in the hexagonal space group P6/mmm with a = 308.6, c = 352.4 pm, and Z = 1. The Mg atoms are arranged in a close-packed layer, and the B atoms form a graphite-like layer with a B–B bond length of a/(3)1/2 = 178.2 pm. These two kinds of layers are interleaved along the c axis, as shown in Fig. 13.3.1(f). In the resulting crystal structure, each B atom is located inside a Mg6 trigonal prism, and each Mg atom is sandwiched between two planar hexagons of B atoms that constitute a B12 hexagonal prism, as illustrated in Fig. 13.3.2. AlB2 has the same crystal structure with a B–B bond length of 175 pm. (2) LaB4 Figure 13.3.3(a) shows a projection of the tetragonal structure of LaB4 along the c axis. The chains of B6 octahedra are directly linked along the c axis and joined laterally by pairs of B2 atoms in the ab plane to form a three-dimensional skeleton. In addition, tunnels accommodating the La atoms run along the c axis. (3) CaB6 The cubic hexaboride CaB6 consists of B6 octahedra, which are linked directly in all six orthogonal directions to give a rigid but open framework, and the Ca atoms occupy cages each surrounded by 24 B atoms, as shown in Fig. 13.3.3(b). The number of valence electrons for a B6 unit can be counted as follows: six electrons are used to form six B–B bonds between the B6 units, and the closo-B6 skeleton is held by three B–B 2c-2e bonds and four BBB 3c-2e bonds, which require 14 electrons. The total number is 6+14 = 20 electrons per B6 unit. Thus in the CaB6 structure each B6 unit requires the transfer of two electrons from metal atoms. However, the complete transfer of 2e per B6 unit is not mandatory for a three-dimensional crystal structure, and theoretical calculations for MB6 (M = Ca, Sr, Ba) indicate a net transfer of only 0.9e to 1.0e. This also explains

466

Structural Chemistry of Selected Elements (a)

(b)

Fig. 13.3.3.

Structures of (a) LaB4 and (b) CaB6 .

(a)

(b)

Fig. 13.3.4.

Structures of (a) cubo-octahedral B12 unit and (b) icosahedral B12 unit. These two units can be interconverted by the displacements of atoms. The arrows indicate shift directions of three pairs of atoms to form additional linkages (and triangular faces) during conversion from (a) to (b), and concurrent shifts of the remaining atoms are omitted for clarity.

why metal-deficient phases M1−x B6 remain stable and why the alkali metal K can also form a hexaboride. (4) High boron-rich metal borides In high boron-rich metal borides, there are two types of B12 units in their crystal structures: one is cubo-octahedral B12 found in YB12 , as shown in Fig. 13.3.4(a); the other is icosahedral B12 in NaB12 , as shown in Fig. 13.3.4(b). These two structural types can be interconverted by small displacements of the B atoms. The arrows shown in Fig. 13.3.4(a) represent the directions of the displacements. (5) Rare-earth metal borides The ionic radii of the rare-earth metals have a dominant effect on the structure types of their crystalline borides, as shown in Table 13.3.2. The “radius” of the 24-coordinate metal site in MB6 is too large (M–B distances are in the range of 215-25 pm) to be comfortably occupied by the later (smaller) lanthanide elements Ho, Er, Tm, and Lu, and these elements form MB4 compounds instead, where the M–B distances vary within the range of 185-200 pm. ¯ with a = 2344 pm and Z = 24. YB66 crystallizes in space group Fm3c The basic structural unit is a thirteen-icosahedra B156 giant cluster in which a central B12 icosahedron is surrounded by twelve B12 icosahedra; the B–B bond distances within the icosahedra are 171.9–185.5 pm, and the intericosahedra

Group 13 Elements Table 13.3.2. Variation of structural types with the ionic radii of rare-earth metals

Cation

radii (pm)

Structural type YB12

Eu2+ La3+ Ce3+ Pr3+ Nd3+ Sm3+ Gd3+ Tb3+ Dy3+ Y3+ Ho3+ Er3+ Tm3+ Yb3+ Lu3+

130 116.0 114.3 112.6 110.9 107.9 105.3 104.0 102.7 101.9 101.5 100.4 99.4 98.5 97.7

+ + + + + + + +

AlB2

+ + + + + + + + +

YB66

ThB4

+ + + + + + + + + + +

+ + + + + + + + + + + + + +

CaB6 + + + + + + +

distances vary between 162.4 and 182.3 pm. Packing of the eight B12 ⊂ (B12 )12 giant clusters in the unit cell generates channels and non-icosahedral bulges that accommodate the remaining 336 boron atoms in a statistical distribution. The yttrium atom is coordinated by twelve boron atoms belonging to four icosahedral faces and up to eight boron atoms located within a bulge. 13.3.2

Non-metal borides

Boron forms a large number of non-metal borides with oxygen and other nonmetallic elements. The principal oxide of boron is boric oxide, B2 O3 . Fused B2 O3 readily dissolves many metal oxides to give borate glasses. Its major application is in the glass industry, where borosilicate glasses find extensive use because of their small coefficient of thermal expansion and easy workability. Borosilicate glasses include Pyrex glass, which is used to manufacture most laboratory glassware. The chemistry of borates and related oxo complexes will be discussed in Section 13.5. (1) Boron carbides and related compounds The potential usefulness of boron carbides has prompted intensive studies of the system B1−x Cx with 0.1 ≤ x ≤ 0.2. The carbides of composition B13 C2 and B4 C, as well as the related compounds B12 P2 and B12As2 , all crystallize ¯ The structure of B13 C2 is derived from in the rhombohedral space group R3m. α-R12 boron with the addition of a linear C–B–C linking group along the [111] direction, as shown in Fig. 13.3.5. The structure of B4 C (a = 520 pm, α = 66◦ ) has been shown to be B11 C(CBC) rather than B12 (CCC), with statistical distribution of a C atom over the vertices of the B11 C icosahedron. For boron phosphide and boron arsenide, a two-atom P–P or As–As link replaces the three-atom chain in the carbides.

467

468

Structural Chemistry of Selected Elements

C B

Fig. 13.3.5.

Structure of B13 C2 . The small dark circles represent B atoms and large circles represent C atoms.

(2) Boron nitrides The common form of BN has an ordered layer structure containing hexagonal rings, as shown in Fig. 13.3.6(a). The layers are arranged so that a B atom in one layer lies directly over a N atom in the next, and vice versa. The B–N distance within a layer is 145 pm, which is shorter than the distance of 157 pm for a B–N single bond, implying the presence of π-bonding. The interlayer distance of 330 pm is consistent with van der Waals interactions. Boron nitride is a good lubricant that resembles graphite. However, unlike graphite, BN is white and an electrical insulator. This difference can be interpreted in terms of band theory, as the band gap in boron nitride is considerably greater than that in graphite because of the polarity of the B–N bond. (a)

(b)

Fig. 13.3.6.

Structures of BN: (a) graphite-like; (b) diamond-like (borazon).

Heating the layered form of BN at ∼2000 K and >50 kbar pressure in the presence of a catalytic amount of Li3 N or Mg3 N2 converts it into a more dense polymorph with the zinc blende structure, as shown in Fig. 13.3.6(b). This cubic form of BN is called borazon, which has a hardness almost equal to that of diamond and is used as an abrasive. As the BN unit is isoelectronic with a C2 fragment, replacement of the latter by the former in various organic compounds leads to azaborane structural analogs. Some examples are shown below. Planar borazine (or borazole) B3 N3 H6 is stabilized by π-delocalization, but it is much more reactive than benzene in view of the partial positive and negative charges on the N and B atoms, respectively.

Group 13 Elements

B N

N B

B

B

N

N

N B

B N

N B

B

B

N

N

N B B N

N B

(3) Boron halides Boron forms numerous binary halides, of which the monomeric trihalides BX3 are volatile and highly reactive. These planar molecules differ from aluminum halides, which form Al2 X6 dimers with a complete valence octet on Al. The difference between BX3 and Al2 X6 is due to the smallness of the B atom. The B atom uses its sp2 hybrid orbitals to form σ bonds with the X atoms, leaving the remaining empty 2pz orbital to overlap with three filled pz orbitals of the X atoms. This generates delocalized π orbitals, three of which are filled with electrons. Thus there is some double-bond character in the B–X bonding that stabilizes the planar monomer. Table 13.3.3 lists some physical properties of BX3 molecules. The energy of the B–F bond in BF3 is 645 kJ mol−1 , which is consistent with its multiple-bond character. All BX3 compounds behave as Lewis acids, the strength of which is determined by the strength of the aforementioned delocalized π bonding; the stronger it is, the molecule more easily retains its planar configuration and the acid strength is weaker. Because of the steadily weakening of π bonding in going from BF3 to BI3 , BF3 is a weaker acid and BI3 is stronger. This order is the reverse of that predicated when the electronegativity and size of the halogens are considered: the high electronegativity of fluorine could be expected to make BF3 more receptive to receiving a lone pair from a Lewis base, and the small size of fluorine would least inhibit the donor’s approach to the boron atom. Salts of tetrafluoroborate, BF− 4 , are readily formed by adding a suitable metal fluoride to BF3 . There is a significant lengthening of the B–F bond from 130 pm in planar BF3 to 145 pm in tetrahedral BF− 4. Among the boron halides, B4 Cl4 is of interest as both B4 H4 and B4 H2− 4 do not exist. Figure 13.3.7 shows the molecular structure of B4 Cl4 , which has a tetrahedral B4 core consolidated by four terminal B–Cl 2c-2e bonds and four BBB 3c-2e bonds on four faces. This structure is further stabilized by σ –π interactions between the lonepairs of Cl atoms and BBB 3c-2e bonds. The Table 13.3.3. Some physical properties of BX3

Molecule

BF3 BCl3 BBr3 BI3 ∗ Quantities

469

B–X bond length (pm)

(rB + rX )∗ (pm)

Bond energy (kJ mol−1 )

mp (K)

bp (K)

130 175 187 210

152 187 202 221

645 444 368 267

146 166 227 323

173 286 364 483

rB and rX represent the covalent radii of B and X atoms, respectively.

Fig. 13.3.7.

Molecular structure of B4 Cl4

470

Structural Chemistry of Selected Elements bond length of B–Cl is 170 pm, corresponding to a single bond, and the bond length of B–B is also 170 pm. 13.4

Boranes and carboranes

13.4.1

Molecular structure and bonding

Boranes and carboranes are electron-deficient compounds with interesting molecular geometries and characteristic bonding features. (1) Molecular structure of boranes and carboranes Figures 13.4.1 and 13.4.2 show the structures of some boranes and carboranes, respectively, that have been established by X-ray and electron diffraction methods. (a)

97º 119.2

(b)

(c)

(e)

(f)

122º

132.9

(d)

Fig. 13.4.1.

Structures of boranes: (a) B2 H6 , (b) B4 H10 , (c) B5 H9 , (d) B6 H10 , (e) B8 H12 , (f) B10 H14 .

(a)

(e) Fig. 13.4.2.

Structures of carboranes: (a) 1,5-C2 B3 H5 , (b) 1,2-C2 B4 H6 , (c) 1,6-C2 B4 H6 , (d) 2,4-C2 B5 H7 , (e)–(g) three isomers of C2 B10 H12 (H atoms are omitted for clarity).

(b)

(c)

(f)

(d)

(g)

Group 13 Elements

+

–

ψ3

ψ3

+

–

H

– ψB1

ψ2

–

+ –

ψ2

ψB2

+

+

ψ1

ψ

–

B

B

ψΗ

+

+

Fig. 13.4.3.

1

– (a)

(b)

(c)

(2) Bonding in boranes In simple covalent bonding theory, there are four bonding types in boranes: (a) normal 2c-2e B–B bond, (b) normal 2c-2e B–H bond, (c) 3c-2e BBB bond (described in Fig. 13.2.4), and (d) 3c-2e BHB bond. The 3c-2e BHB bond is constructed from two orbitals of B1 and B2 atoms (ψB1 and ψB2 , which are spx hybrids) and ψH (1s orbital) of the H atom. The combinations of these three atomic orbitals result in three molecular orbitals: 1 1 1 ψH ψB + ψB + 2 1 2 2 (2)1/2 1 ψ2 = (ψB1 − ψB2 ) (2)1/2 1 1 1 ψ3 = ψB1 + ψB2 − ψH . 2 2 (2)1/2 ψ1 =

The orbital overlaps and relative energies are illustrated in Fig. 13.4.3. Note that ψ1 , ψ2 , and ψ3 are bonding, nonbonding, and antibonding molecular orbitals, respectively. For the 3c-2e BHB bond, only ψ1 is filled with electrons. (3) Topological description of boranes The overall bonding in borane molecules or anions is sometimes represented by a 4-digit code introduced by Lipscomb, the so-called styx number, where s is the number of 3c-2e BHB bonds, t is the number of 3c-2e BBB bonds, y is the number of normal B–B bonds, and x is the number of BH2 groups. H

B B

B

B s

471

B

B

B t

y

H

B

H

x

The molecular structural formulas of some boranes and their styx codes are shown in Fig. 13.4.4.

The 3c-2e BHB bond: (a) orbitals overlap, (b) relative energies, and (c) simple representation.

472

Structural Chemistry of Selected Elements H

H

H

H

H

B

H

B

H

H

H

H

H B

B

B

H

B H

Fig. 13.4.4.

B

H

B

H

B H

B

H H

H

B

B

B B

H B H

H

H

H

H

H

H

H B

B5H9 4120

H H

B

B

H

H

B H

B

H

H

B6H10 4220

Molecular structural formulas and styx codes of some boranes.

H

H

H

H

H B

B

B4H10 4012

H H

H

H

B

H

B2H6 2002

H

H

B

B7H15 6122

H

H H

The following simple rules must hold for the borane structures: (a) Each B atom has at least a terminal H atom attached to it. (b) Every pair of boron atoms which are geometric neighbors must be connected by a B–B, BHB, or BBB bond. (c) Every boron atom uses four valence orbitals in bonding to achieve an octet configuration. (d) No two boron atoms may be bonded together by both 2c-2e B–B and 3c-2e BBB bonds, or by both 2c-2e B–B and 3c-2e BHB bonds. 13.4.2

Bond valence in molecular skeletons

The geometry of a molecule is related to the number of valence electrons in it. According to the valence bond theory, organic and borane molecules composed of main-group elements owe their stability to the filling of all four valence orbitals (ns and np) of each atom, with eight valence electrons provided by the atom and those bonded to it. Likewise, transition-metal compounds achieve stability by filling the nine valence orbitals [(n–1)d, ns, and np] of each transition-metal atom with 18 electrons provided by the metal atom and the surrounding ligands. In molecular orbital language, the octet and 18-electron rules are rationalized in terms of the filling of all bonding and nonbonding molecular orbitals and the existence of a large HOMO-LUMO energy gap. Consider a molecular skeleton composed of n main-group atoms, Mn , which takes the form of a chain, ring, cage, or framework. Let g be the total number of valence electrons of the molecular skeleton. When a covalent bond is formed between two M atoms, each of them effectively gains one electron in its valence shell. In order to satisfy the octet rule for the whole skeleton, 12 (8n − g) electron pairs must be involved in bonding between the M atoms. The number of these bonding electron pairs is defined as the “bond valence” b of the molecular skeleton: b = 12 (8n − g).

(13.4.1)

Group 13 Elements When the total number of valence electrons in a molecular skeleton is less than the number of valence orbitals, the formation of normal 2c-2e covalent bonds is insufficient to compensate for the lack of electrons. In this type of electron-deficient compound there are usually found 3c-2e bonds, in which three atoms share an electron pair. Thus one 3c-2e bond serves to compensate for the lack of four electrons and corresponds to a bond valence value of 2, as discussed in 13.2. There is an enormous number of compounds that possess metal–metal bonds. A metal cluster may be defined as a polynuclear compound in which there are substantial and directed bonds between the metal atoms. The metal atoms of a cluster are also referred to as skeletal atoms, and the remaining non-metal atoms and groups are considered as ligands. According to the 18-electron rule, the bond valence of a transition metal cluster is b = 12 (18n − g).

(13.4.2)

If the bond valence b calculated from (13.4.1) and (13.4.2) for a cluster Mn matches the number of connecting lines drawn between pairs of adjacent atoms in a conventional valence bond structural formula, the cluster is termed “electron-precise.” For a molecular skeleton consists of n1 transition-metal atoms and n2 maingroup atoms, such as transition-metal carboranes, its bond valence is b = 12 (18n1 + 8n2 − g).

(13.4.3)

The bond valence b of a molecular skeleton can be calculated from expressions (13.4.1) to (13.4.3), in which g represents the total number of valence electrons in the system. The g value is the sum of: (1) the number of valence electrons of the n atoms that constitute the molecular skeleton Mn , (2) the number of electrons donated by the ligands to Mn , and (3) the number of net positive or negative charges carried by Mn , if any. The simplest way to count the g value is to start from uncharged skeletal atoms and uncharged ligands. Ligands such as NH3 , PR3 , and CO each supply two electrons. Non-bridging halogen atoms, H atom, and CR3 and SiR3 groups are one-electron donors. A µ2 -bridging halogen atom contributes three electrons, and a µ3 bridging halogen atom donates five electrons. Table 13.4.1 lists the number of electrons contributed by various ligands, depending on their coordination modes. 13.4.3

Wade’s rules

For boranes and carboranes, the terms closo, nido, arachno, and hypho are used to describe their molecular skeletons with reference to a series of increasingly open deltahedra. Boranes of the nido, arachno, and hypho types are compounds based on formulas Bn Hn+4 , Bn Hn+6 , and Bn Hn+8 , respectively. The structures

473

474

Structural Chemistry of Selected Elements Table 13.4.1. Number of electrons supplied by ligands to a molecular skeleton

Ligand

Coordinate mode∗

No. of electrons

H B CO CR CR2 CR3 , SiR3 η2 –C2 R2 η2 –C2 R4 η5 –C5 R5 η6 –C6 R6 C, Si N, P, As, Sb

µ1 , µ2 , µ3 int µ1 , µ2 , µ3 µ3 , µ4 µ1 µ1 , µ2 µ1 µ1 µ1 µ1 int int

1 3 2 3 2 1 2 2 5 6 4 5

Ligand

NR3 , PR3 NCR NO OR, SR OR, SR O, S, Se, Te O, S, Se, Te O, S F, Cl, Br, I F, Cl, Br, I Cl, Br, I PR

Coordinate mode∗ µ1 µ1 µ1 µ1 µ2 µ2 µ3 int µ1 µ2 µ3 µ3 , µ4

No. of electrons 2 2 3 1 3 2 4 6 1 3 5 4

The skeletal atoms are considered to be uncharged. ∗ µ = terminal ligand, µ = ligand bridging two atoms, µ = ligand bridging three 1 2 3 atoms, int = interstitial atom.

of nido-boranes are analogous to the corresponding closo compounds with the exception that one vertex is missing. For example, in B5 H9 , five B atoms are located at the vertices of an octahedron whereas the sixth vertex is empty. Likewise, the arrangement of n skeletal atoms of arachno compounds is referred to a deltahedron having (n + 2) vertices; for instance, the B atoms in B4 H10 lie at four vertices of an octahedron in which two adjacent vertices are not occupied. For hypothetical Bn Hn+8 and its isoelectronic equivalent Bn Hn+62− , the cluster skeleton is a n-vertex deltahedron with three missing vertices. (a)

(b)

(c)

Fig. 13.4.5.

Structural relationship between (a) closo-B7 H2− 7 , (b) nido-B6 H10 and (c) arachno-B5 H11 .

Figure 13.4.5 shows the relations between (a) closo-B7 H72− , (b) nido-B6 H10 , and (c) arachno-B5 H11 . The structure of closo-B7 H72− is a pentagonal bipyramid. In nido-B6 H10 , the B atoms are located at six vertices of the pentagonal bipyramid, and one vertex on the C5 axis is not occupied. In arachno-B5 H11 , two vertices of the pentagonal bipyramid, one axial and one equatorial, are not occupied. Historically, a scheme of skeletal electron-counting was developed to rationalize the structures of boranes and their derivatives, to which the following Wade’s rules are applicable.

Group 13 Elements (a)

(b)

PMe3

B

Me3P H

H

H

H H B H

B B H

(c)

H B

B

B

C

B

H H

H

C

C

H

CH2CN

B

H B

C

B

C(CN)2

C

B

H

C(CN)2

H

B

B B

475

B

B

B

Fig. 13.4.6.

− 2 Molecular structures of some hypho cluster systems: (a) B5 H9 (PMe3 )2 ; (b) (NCCH2 )C3 B6 H− 12 ; (c) [µ -{C(CN)2 }2 ]C2 B7 H12 . In carboranes (b) and (c), for clarity only bridging and extra H atoms are included, and all exo H atoms attached to the vertices are omitted.

(1) A closo-deltahedral cluster with n vertices is held together by (n + 1) bonding electron pairs. (2) A nido-deltahedral cluster with n vertices is held together by (n+2) bonding electron pairs. (3) An arachno-deltahedral cluster with n vertices is held together by (n + 3) bonding electron pairs. (4) A hypho-deltahedral cluster with n vertices is held together by (n + 4) bonding electron pairs. Boranes and carboranes of the hypho type are quite rare. The prototype hypho-borane B5 H112− has been isolated, and its proposed structure is analogous to that of the isoelectronic analog B5 H9 (PMe3 )2 (Fig. 13.4.6(a)), which was established by X-ray crystallography. The 9-vertex hypho tricarbaborane cluster anion (NCCH2 )-1,2,5-C3 B6 H12− shown in Fig. 13.4.6(b) has 13 skeletal pairs, and accordingly it may be considered as derived from an icosahedron with three missing vertices. Similarly, in endo-6-endo-7-[µ2 -{C(CN)2 }2 ]-arachno6,8-C2 B7 H12− [Fig. 13.4.6(c)], the C2 B7 -fragment of the cluster anion can be viewed as a 13-electron pair, 9-vertex hypo system with an exo-polyhedral TCNE substituent bridging a C atom and a B atom at the open side. 13.4.4

Chemical bonding in closo-boranes

Boranes of the general formula Bn Hn2− and isoelectronic carboranes such as CBn−1 Hn− and C2 Bn−2 Hn have closo structures, in which n skeletal B and C atoms are located at the vertices of a polyhedron bounded by trianglular faces (deltahedron). For the Bn Hn2− closo-boranes b = 21 [8n − (4n + 2)] = 2n − 1.

(13.4.4)

From the geometrical structures of closo-boranes, s and x of the styx code are both equal to 0. Each 3c–2e BBB bond has a bond valence value of 2. Thus, b = 2t + y.

(13.4.5)

476

Structural Chemistry of Selected Elements Combining expressions (13.4.4) and (13.4.5) leads to 2t + y = 2n − 1.

(13.4.6)

When the number of electron pairs of the molecular skeleton is counted, one gets t + y = n + 1.

(13.4.7)

Hence from (13.4.6) and (13.4.7), t = n − 2,

(13.4.8)

y = 3,

(13.4.9)

so that each closo-borane Bn Hn2− has exactly three B–B bonds in its valence bond structural formula. 2− Table 13.4.2. Bond valence and other parameters for Bn Hn

n in Bn Hn2−

styx code

5 6 7 8 9 10 11 12

0330 0430 0530 0630 0730 0830 0930 0,10,3,0

Bond valence b

No. of edges = 3t

No. of faces = 2t

t + y (No. of skeletal electron pairs)

9 11 13 15 17 19 21 23

9 12 15 18 21 24 27 30

6 8 10 12 14 16 18 20

6 7 8 9 10 11 12 13

Table 13.4.2 lists the bond valence of Bn Hn2− and other parameters; n starts from 5, not from 4, as B4 H42− would need t = 2 and y = 3, which cannot satisfy rule (d) for a tetrahedron. Figure 13.4.7 shows the localized bonding (a)

(b) 1

2

5

4

4

The B–B and BBB bonds in (a) B5 H52− , (b) B6 H62− , and (c) B10 H102− ; for each

molecule both the front and back sides of a canonical structure are displayed. The molecular skeleton of B12 H122− is shown in Fig.13.2.2, and the bonding is shown in Fig.13.2.4.

(c)

5

4

4

3

3

B5H52– Fig. 13.4.7.

2

2

3

1

1

1

1 7 8

3

6

6

5

5

2

9

4

10 4

B10H10

2–

3

B6H62–

1

2

3

6

2

Group 13 Elements description (in one canonical form) for some closo-boranes. The charge of −2 in Bn Hn2− is required for consolidating the n BH units into a deltahedron. Except for B5 H52− , the bond valence b is always smaller than the number of edges of the polyhedron. In the Bn skeleton of closo-boranes, there are (n − 2) 3c-2e BBB bonds and three normal B–B bonds, which amounts to (n − 2) + 3 = n + 1 electron pairs. Some isoelectronic species of C2 B10 H12 , such as CB11 H12− , NB11 H12 , and their derivatives, are known. Since they have the same number of skeletal atoms and the same bond valence, these compounds are isostructural. 13.4.5

Chemical bonding in nido- and arachno-boranes

Using the styx code and bond valence to describe the structures of nido-boranes or carboranes, the bond valence b is equal to b = 12 [8n − (4n + 4)] = 2n − 2,

(13.4.10)

b = s + 2t + y.

(13.4.11)

Combining expressions (13.4.10) and (13.4.11) leads to s + 2t + y = 2n − 2.

(13.4.12)

The number of valence electron pairs for nido Bn Hn+4 is equal to 12 (4n+4) = 2n + 2, in which n + 4 pairs are used to form B–H bonds and the remaining electron pairs used to form 2c–2e B–B bonds (y) and 3c–2e BBB bonds (t). Thus, t + y = (2n + 2) − (n + 4) = n − 2.

(13.4.13)

The number of each bond type in nido-Bn Hn+4 are obtained from expressions (13.4.12) and (13.4.13): t = n − s,

(13.4.14)

x + s = 4.

(13.4.16)

y = s − 2,

(13.4.15)

The stability of a molecular species with open skeleton may be strengthened by forming 3c-2e bond(s). In a stable nido-borane, neighboring H–B–H and B–H groups always tend to be converted into the H–BHB–H system:

H

B H

B H

H

B

B H

H

477

478

Structural Chemistry of Selected Elements Table 13.4.3. The styx codes of some nido-boranes

Borane

s t y x b = s + 2t + y

B4 H8

B5 H9

B6 H10

B7 H11

B8 H12

B9 H13

B10 H14

4 0 2 0 6

4 1 2 0 8

4 2 2 0 10

4 3 2 0 12

4 4 2 0 14

4 5 2 0 16

4 6 2 0 18

Thus, in nido-borane, x = 0, s = 4, and t =n−4

(13.4.17)

y = 2.

(13.4.18)

Table 13.4.3 lists the styx code and bond valence of some nido-boranes, and Fig. 13.4.8 shows the chemical bonding in their skeletons. (a)

(b)

(c)

(d)

(e)

Fig. 13.4.8.

Chemical bonding in the skeletons of some nido-boranes (large circles represent BH group, small circles represent H atoms in BHB bonds): (a) B4 H8 (4020), (b) B5 H9 (4120), (c) B6 H10 (4220), (d) B8 H12 (4420), (e) B10 H14 (4620).

For the arachno-boranes, Bn Hn+6 , the relations between styx code and n are as follows: t =n−s

y =s−3

x + s = 6.

(13.4.19) (13.4.20) (13.4.21)

According to the octet and 18-electron rules, when one C atom replaces one BH group in a borane, the g value and b value are unchanged, and the structure

Group 13 Elements (a)

(b)

(c)

(d)

(e)

(f)

479

Fig. 13.4.9.

P Ir

of the carborane is the same as that of the borane. Likewise, when one transitionmetal atom replaces one BH group, the bond valence counting of (13.4.3) also remains unchanged. Figure 13.4.9 shows two series of compounds, which have the same b value in each series. 13.4.6

Electron-counting scheme for macropolyhedral boranes: mno rule

A generalized electron-counting scheme, known as the mno rule, is applicable to a wide range of polycondensed polyhedral boranes and heteroboranes, metallaboranes, metallocenes, and any of their combinations. According to this mno rule, the number of electron pairs N necessary for a macropolyhedral system to be stable is N = m + n + o + p − q, where m = the number of polyhedra, n = the number of vertices, o = the number of single-vertex-sharing connections, p = the number of missing vertices, and q = the number of capping vertices. For a closo macropolyhedral borane cluster, the rule giving the required number of electron pairs is N = m + n. Some examples illustrating the application of the mno rule are given in Table 13.4.4, which makes reference to the structures of compounds shown in Fig. 13.4.10. B20 H16 is composed of two polyhedra sharing four atoms. The (m + n) electron pair count is 2 + 20 = 22, which is appropriate for a closo structure stabilized by 22 skeletal electron pairs (16 from 16 BH groups and 6 from four B

Structures of corresponding boranes, carboranes, and metalloboranes having the same bond valence: (a) B5 H9 , (b) CB4 H8 , and (c) B3 H7 [Fe(CO)3 ]2 , b = 8; (d) B6 H10 , (e) CB5 H9 , and (f) B5 H8 Ir(CO)(PPh3 )2 , b = 10.

480

Structural Chemistry of Selected Elements Table 13.4.4. Application of the mno rule for electron counting in some condensed polyhedral boranes and related compounds∗

Formula

B20 H16 (C2 B10 H11 )2 [(C2 B9 H11 )2Al]− [B21 H18 ]− Cp2 Fe Cp∗ IrB18 H20 [Cp∗ IrB18 H19 S]− Cp∗2 Rh2 S2 B15 H14 (OH) (CpCo)3 B4 H4

Structure in Fig. 3.4.10

m

n

o

p

q

N

BH

B

CH

Hb

α

β

x

(a) (b) (c) (d) (e) (f) (g) (h) (i)

2 2 2 2 2 3 3 4 4

20 24 23 21 11 24 25 29 22

0 0 1 0 1 1 1 2 3

0 0 0 0 2 3 3 5 3

0 0 0 0 0 0 0 0 1

22 26 26 23 16 31 32 40 31

16 18 18 18 0 15 16 13 4

6 2 0 4.5 0 4.5 3 3 0

0 6 6 0 15 7.5 7.5 15 22.5

0 0 0 0 0 2.5 1.5 2 0

0 0 1.5 0 1 1.5 1.5 3 4.5

0 0 0 0 0 0 2 4 0

0 0 0.5 0.5 0 0 0.5 0 0

∗ BH = number of electron pairs from BH groups, B = number of electron pairs from B atoms, CH = number of electron pairs from CH groups, α = number of electron pairs from metal center(s), β = number of electron pairs from main-group hetero atom, Hb = number of electron pairs from bridging hydrogen atoms, x = number of electron pairs from the charge. Also, BH (or CH) can be replaced by BR (or CR).

atoms). In (C2 B10 H11 )2 , which consists of two icosahedral units connected by a B–B single bond, the electron count is simply twice that of a single polyhedron. The 26 skeletal electron pairs are provided by 18 BH groups (18 pairs), 2 B atoms (2 pairs, B–B bond not involved in cluster bonding), and 4 CH groups (6 pairs, 3 electrons from each CH group). The structure of [(C2 B9 H11 )2Al]− is constructed from condensation of two icosahedra through a common vertex. The required skeletal electron pairs are contributed by 18 BH groups (18 pairs), 4 CH groups (6 pairs), the Al atom (1.5 pairs), and the anionic charge (0.5 pair). The polyhedral borane anion B21 H18− has a shared triangular face. Its 18 BH groups, 3 B atoms, and the negative charge provide 18 + 4.5 + 0.5 = 23 skeletal pairs, which fit the mno rule with m+n = 2+21. For ferrocene, which has 16 electron pairs (15 from 10 CH groups and 1 from Fe), the mno rule suggests a molecular skeleton with two open (nido) faces (m + n + o + p = 2 + 11 + 1 + 2 = 16). The metalloborane [Cp∗ IrB18 H20 ] is condensed from three nido units. The mno rule gives 31 electron pairs, and the molecular skeleton is stabilized by electron pairs from 15 BH groups (15), 5 CH groups (7.5), 3 shared B atoms (4.5), 5 bridging H atoms (2.5), and the Ir atom [ 12 (9 − 6)] = 1.5; 6 electrons occupying 3 nonbonding metal orbitals]. Addition of a sulfur atom as a vertex to the above cluster leads to [Cp∗ IrB18 H19 S]− , which requires 32 electron pairs. The electrons are supplied by the S atom (4 electrons, as the other 2 valence electrons occupy an exo-cluster orbital), 16 BH groups, 2 shared B atoms, 3 bridging H atoms, the Ir atom, and the negative charge. The cluster compound [Cp∗2 Rh2 S2 B15 H14 (OH)] contains a nido {RhSB8 H7 } unit and an arachno {RhSB9 H8 (OH)} unit conjoined by a common B–B edge. The mno rule leads to 40 electron pairs, which are supplied by 13 BH groups (13), 2 B atoms (3), 10 CH groups (15), 4 bridging H atoms (2), 2 Rh atoms (3), and 2 S atoms (4). In the structure of (CpCo)3 B4 H4 , 1 B atom caps the Co3 face of a Co3 B3 octahedron, and the 31 electron pairs are supplied by 4 BH groups (4), 15 CH groups (22.5), and 3 Co atoms (4.5).

Group 13 Elements (a)

481

(b)

(c)

(d)

(e) Fe

Al

(f)

(g)

Ir

Ir

S

C (h)

Fig. 13.4.10.

(i)

C

Co

Rh OH

13.4.7

S

Electronic structure of β-rhombohedral boron

In Section 13.2 and Fig. 13.2.5, the structure of β-R105 boron is described in terms of large B84 (B12a @B12 @B60 ) clusters and B10 –B–B10 units. Each B10 unit of C3v symmetry is fused with three B6 half-icosahedra from three adjacent B84 clusters, forming a B28 cluster composed of four fused icosahedra, as shown in Fig. 13.4.11(a). A pair of such B28 clusters are connected by a six-coordinate B atom to form a B57 (B28 –B–B28 ) unit. To understand the subtlety and electronic structure of the complex covalent network of β-R105 boron, it is useful to view the contents of the unit cell [Fig. 13.4.11(b)] as assembled from B12a (at the center of a B84 cluster) and B57 (lying on a C3 axis) fragments connected by 2c-2e bonds. The electronic requirement of the B57 unit can be assessed by saturating the dangling valencies with hydrogen atoms, yielding the molecule B57 H36 . According to the mno rule, 8 + 57 + 1 = 66 electron pairs are required for stability, but the number available is 67.5 [36 (from 36 BH) + (21 × 3)/2 (from 21B)]. Thus the B57 H36 polyhedral skeleton needs to get rid of three electrons to achieve stability, whereas the B12a H12 skeleton requires two additional electrons for sufficiency. As the unit cell contains four B12a and one B57 fragments, the idealized structure of β-rhombohedral boron has a net deficiency of five electrons.

Structure of condensed polyhedral boranes, metallaboranes, and ferrocene listed in Table 13.4.4: (a) B20 H16 , (b) (C2 B10 H11 )2 , (c) [(C2 B9 H11 )2Al]− , (d) [B21 H18 ]− , (e) Cp∗ 2 Fe, (f) Cp∗ IrB18 H20 , (g) [Cp∗ IrB18 H19 S]− , (h) Cp∗ 2 Rh2 S2 B15 H14 (OH), and (i) (CpCo)3 B4 H4 . (The Me group of Cp∗ and H atoms is not shown.)

482

Structural Chemistry of Selected Elements (a)

(b) (b)

B28 unit B12 unit B atom hole Fig. 13.4.11.

Structure of β-R105 boron. (a) Three half-icosahedra of adjacent B84 clusters fuse with a B10 unit to form a B28 unit. (b) Unit cell depicting the B12 units at the vertices and edge centers, leaving the B28 –B–B28 unit along the main body diagonal. Holes of three different types are also indicated.

X-ray studies have established that β-R105 boron has a very porous (only 36% of space is filled in the idealized model) and defective structure with the presence of interstitial atoms and partial occupancies. The B57 fragment can dispose of excess electrons by removal of some vertices to form nido or arachno structures, and individual B12a units can gain electrons by incorporating capping vertices that are accommodated in interstitial holes (see Fig. 13.4.11(b)). 13.4.8

Persubstituted derivatives of icosahedral borane B12 H122−

The compound Cs8 [B12 (BSe3 )6 ] is prepared from the solid-state reaction between Cs2 Se, Se, and B at high temperature. In the anion [B12 (BSe3 )6 ]8− , each trigonal planar BSe3 unit is bonded to a pair of neighboring B atom in the B12 skeleton, as shown in Fig. 13.4.12. It is the first example of bonding between a chalcogen and an icosahedral B12 core. The point group of [B12 (BSe3 )6 ]8− is D3d . Icosahedral B12 H122− can be converted to [B12 (OH)12 ]2− , in which the 12 hydroxy groups can be substituted to form carboxylic acid esters [B12 (O2 CMe)12 ]2− , [B12 (O2 CPh)12 ]2− , and [B12 (OCH2 Ph)12 ]2− . The sequential twoelectron oxidation of [B12 (OCH2 Ph)12 ]2− with Fe3+ in ethanol affords hyper closo-B12 (OCH2 Ph)12 as a dark-orange crystal. An X-ray diffraction study of hypercloso-B12 (OCH2 Ph)12 revealed that the molecule has distorted icosahedral

Group 13 Elements

483

Fig. 13.4.12.

Structure of [B12 (BSe3 )6 ]8− .

geometry (D3d ). The term hypercloso refers to an n-vertex polyhedral structure having fewer skeletal electron pairs than (n + 1) as required by Wade’s rule. 13.4.9

Boranes and carboranes as ligands

Many boranes and carboranes can act as very effective polyhapto ligands to form metallaboranes and metallacarboranes. Metallaboranes are borane cages containing one or more metal atoms in the skeletal framework. Metallacarboranes have both metal and carbon atoms in the cage skeleton. In contrast to the metallaboranes, syntheses of metallacarboranes via low- or room-temperature metal insertion into carborane anions in solution are more controllable, usually occurring at a well-defined C2 Bn open face to yield a single isomer.

o-C2B10H12 –BH

+2e–

+4e–

Fig. 13.4.13.

Conversion of icosahedral carborane o-C2 B10 H12 to nido-C2 B9 H112− ,

2–

nido-C2B9H11

nido-C2B10H122–

4–

arachno-C2B10H12

The icosahedral carborane cage C2 B10 H12 can be converted to the nidoC2 B9 H112− , nido-C2 B10 H122− , or arachno-C2 B10 H124− anions, as shown in Fig. 13.4.13. Nido-C2 B9 H112− has a planar five-membered C2 B3 ring with delocalized π orbitals, which is similar to the cyclopentadienyl ring. Likewise, nido-C2 B10 H122− has a nearly planar C2 B4 six-membered ring and delocalized π orbitals, which is analogous to benzene. Arachno-C2 B10 H124− has a boat-like C2 B5 bonding face in which the five B atoms are coplanar and the two C atoms lie approximately 60 pm above this plane.

nido-C2 B10 H122− , and arachno-C2 B10 H124− .

484

Structural Chemistry of Selected Elements The similarity between the C2 B3 open face in nido-C2 B9 H112− and the C5 H5− anion implies that the dicarbollide ion can act as an η5 -coordinated ligand to form sandwich complexes with metal atoms, which are analogous to the metallocenes. Likewise, the C2 B4 open face in nido-C2 B10 H122− is analogous to benzene and it may be expected to function as an η6 -ligand. A large number of metallacarboranes and polyhedral metallaboranes of s-, p-, d-, and f-block elements are known. In these compounds, the carboranes and boranes act as polyhapto ligands. The domain of metallaboranes and metallacarboranes has grown enormously and engenders a rich structural chemistry. Some new advances in the chemistry of metallacarboranes of f-block elements are described below. The full-sandwich lanthanacarborane [Na(THF)2 ][(η5 -C2 B9 H11 )2 La(THF)2 ] has been prepared by direct salt metathesis between Na2 [C2 B9 H11 ] and LaCl3 in THF. The structure of the anion is shown in Fig. 13.4.14(a). The average Lacage atom distance is 280.4 pm, and the ring centroid–La–ring centroid angle is 132.7◦ . The structure of samaracarborane [η5 :η6 -Me2 Si(C5 H4 )(C2 B10 H11 )] Sm(THF)2 is shown in Fig. 13.4.14(b), in which the Sm3+ ion is surrounded by an η5 -cyclopentadienyl ring, η6 -hexagonal C2 B4 face of the C2 B10 H11 cage, and two THF molecules in a distorted tetrahedral manner. The ring centroid– Sm–ring centroid angle is 125.1◦ and the average Sm–cage atom and Sm–C(C5 ring) distances are 280.3 and 270.6 pm, respectively. Figure 13.4.14(c) shows the coordination environment of the Er atom in the {η7 -[(C6 H5 CH2 )2 (C2 B10 H10 )]Er(THF)}2 ·{Na(THF)3 }2 ·2THF. The Er atom is coordinated by η7 -[arachno-(C6 H5 CH2 )2 C2 B10 H10 ]4− and σ -bonded to two (a)

(b)

Sm

Si

La

O

O

(c)

(d)

Fig. 13.4.14.

Structure of some metallacarboranes of f-block elements: (a) [η5 -C2 B9 H11 ]2 La(THF)2 ]− , (b) [η5 :η6 Me2 Si(C5 H4 )(C2 B10 H11 )]Sm(THF)2 , (c) {[η7 C2 B10 H10 (CH2 C6 H5 )2 ]Er(THF)− }, (d) [(η7 -C2 B10 H12 )(η6 C2 B10 H12 )U]24− .

O

H Er

O

U

H

Group 13 Elements

485

B–H groups from a neighboring [arachno-(C6 H5 CH2 )2 C2 B10 H10 ]4− ligand and one THF molecule. The average Er–B(cage) distance is 266.5 pm, and that for the Er–C(cage) is 236.6 pm. The compound [{(η7 -C2 B10 H12 )(η6 -C2 B10 H12 )U}2 {K2 (THF)5 }]2 has been prepared from the reaction of o-C2 B10 H12 with excess K metal in THF, followed by treatment with a THF suspension of UCl4 . In this structure each U4+ ion is bonded to η6 -nido-C2 B10 H122− and η7 -arachno-C2 B10 H124− , and coordinated by two B–H groups from the C2 B5 bonding face of a neighboring arachnoC2 B10 H124− ligand, as shown in Fig. 13.4.14(d). This is the first example of an actinacarborane bearing a η6 - C2 B10 H122− ligand. 13.4.10

Carborane skeletons beyond the icosahedron

Recent synthetic studies have shown that carborane skeletons larger than the icosahedron can be constructed by the insertion of additional BH units. The reaction scheme and structure motifs of these carborane species are shown in Fig. 13.4.15. Treatment of 1,2-(CH2 )3 -1,2-C2 B10 H10 (1) with excess lithium metal in THF at room temperature gave {[(CH2 )3 -1,2-C2 B10 H10 ][Li4 (THF)5 ]} 2 (2) in 85% yield. X-ray analysis showed that, in the crystalline state, both the hexagonal and pentagonal faces of the “carbon-atoms-adjacent” arachno-carborane tetra-anion in 2 are capped by lithium ions, which may in principle be substituted by BH groups. The reaction of 2 with 5.0 equivalents of HBBr2 ·SMe2 in toluene at −78 ◦ C to 25 ◦ C yielded a mixture of a 13-vertex closo-carborane (CH2 )3 C2 B11 H11 (3, 32%), a 14-vertex closo-carborane (CH2 )3 C2 B12 H12 (4, 7%); 1 (2%). Closo-carboranes 3 and 4 can be converted through reduction reaction into their nido-carborane salts {[(CH2 )3 C2 B11 H11 ][Na2 (THF)4 ]}n (5) and {[(CH2 )3 C2 B12 H12 ][Na2 (THF)4 ]}n (6), respectively. Compound 4 can also be prepared from the reaction of 5 with HBBr2 ·SMe2 , whose cage skeleton is a bicapped hexagonal antiprism. Quite different from the planar open faces in nido-C2 B9 H112− and nidoC2 B10 H122− , the open faces of the 13- and 14-vertex nido cages in 5 and 6 are

excess Li

[Li4(THF)5]

THF

HBBr2·SMe2 toluene

2

1

[Na2(THF)4]

6

3 excess Na

HBBr2.SMe2

THF

toluene

4

excess Na THF

[Na2(THF)4]

5

Fig. 13.4.15.

Synthesis of “carbon-atoms-adjacent” 13- and 14-vertex closo-carboranes and nido-carborane anions. From L. Deng, H.-S. Chan and Z. Xie, Angew. Chem. Int. Ed. 44, 2128–31 (2005).

486

Structural Chemistry of Selected Elements (a)

(b)

(c)

P(1) Ni

Ru

Ru

Fig. 13.4.16.

Structure of some metallacarboranes with 14 and 15 vertices: (a) [η5 -(CH2 )3 C2 B11 H11 ]Ni(dppe); (b) [η6 -(CH2 )3 C2 B11 H11 ]Ru(p-cymene); (c) [η6 -(CH2 )3 C2 B12 H12 ]Ru(p-cymene). From L. Deng, H.-S. Chan and Z. Xie, J. Am. Chem. Soc. 128, 5219–30 (2006); and L. Deng, J. Zhang, H.-S. Chan and Z. Xie, Angew. Chem. Int. Ed. 45, 4309–13 (2006).

bent five-membered rings. Despite this, they can be capped by metal atoms to give metallacarboranes with 14 and 15 vertices, respectively. Figure 13.4.16 shows some examples of these novel metallacarboranes. The complexes [η5 -(CH2 )3 C2 B11 H11 ]Ni(dppe) and [η6 -(CH2 )3 C2 B11 H11 ] Ru(p-cymene) were prepared by the reactions of 5 with (dppe)NiCl2 and [(p-cymene)RuCl2 ]2 , respectively. Although both of them are 14-vertex metallacarboranes having a similar bicapped hexagonal antiprismatic cage geometry, the coordination modes of their carborane anions are quite different: the carborane anion [(CH2 )3 C2 B11 H11 ]2− is η5 -bound to the Ni atom in the nickelacarborane [Fig. 13.4.16(a)], whereas an η6 -bonding fashion is observed in the ruthenacarborane with an average Ru-cage atom distance of 226.6 pm [Fig. 13.4.16(b)]. Figure 13.4.16(c) shows the structure of a 15-vertex ruthenacarborane, [(CH2 )3 C2 B12 H12 ]Ru(p-cymene), which was synthesized by the reaction of 6 with [(p-cymene)RuCl2 ]2 . Similar to that in the above-mentioned 14-vertex ruthenacarborane, the carborane moiety [(CH2 )3 C2 B12 H12 ]2− in this 15-vertex ruthenacarborane is also η6 -bound to the Ru atom, forming a hexacosahedral structure. The distances of Ru–arene(cent) and Ru–CB5 (cent) are 178 and 141 pm, respectively. This 15-vertex ruthenacarborane has the largest vertex number in the metallacarborane family known at present.

Fig. 13.5.1.

Structure of layer of B(OH)3 (B–O 136.1 pm, O–H· · · O 272 pm).

13.5

Boric acid and borates

13.5.1

Boric acid

Boric acid, B(OH)3 , is the archetype and primary source of oxo-boron compounds. It is also the normal end product of hydrolysis of most boron compounds. It forms flaky, white and transparent crystals, in which the BO3 units are joined to form planar layers by O–H· · · O hydrogen bonds, as shown in Fig. 13.5.1. Boric acid is a very weak monobasic acid (pKa = 9.25). It generally behaves not as a Brønsted acid with the formation of the conjugate-base [BO(OH)2 ]− , but rather as a Lewis acid by accepting an electron pair from an OH− anion to

Group 13 Elements

487

form the tetrahedral species [B(OH)4 ]− : (HO)3 B +

[sp2 +p(unoccupied)]

: OH− −→ B(OH)4− . sp3

Thus this reaction is analogous to the acceptor–donor interaction between BF3 and NH3 : F3 B + [sp2 +p(unoccupied)]

: NH3 −→ F3 B ← NH3 . sp3

In the above two reactions, the hybridization of the B atom changes from sp2 (reactant) to sp3 (product). Partial dehydration of B(OH)3 above 373 K yields metaboric acid, HBO2 , which consists of trimeric units B3 O3 (OH)3 . Orthorhombic metaboric acid is built of discrete molecules B3 O3 (OH)3 , which are linked into layers by O– H· · · O bonds, as shown in Fig. 13.5.2. In dilute aqueous solution, there is an equilibrium between B(OH)3 and B(OH)− 4: − B(OH)3 + 2H2 O ? A H3 O+ + B(OH)4 .

At concentrations above 0.1 M, secondary equilibria involving condensation reactions of the two dominant monomeric species give rise to oligomers such as the triborate monoanion [B3 O3 (OH)4 ]− , the triborate dianion [B3 O3 (OH)5 ]2− , the tetraborate [B4 O5 (OH)4 ]2− , and the pentaborate [B5 O6 (OH)4 ]− . In (Et4 N)2 [BO(OH)2 ]2 ·B(OH)3 ·5H2 O, the conjugate acid–base pair B(OH)3 and dihydrogen borate [BO(OH)2 ]− coexist in the crystalline state. In the crystal structure of the inclusion compound Me4 N+ [BO(OH)2 ]− · 2(NH2 )2 CO·H2 O, the BO(OH)2− , (NH2 )2 CO, and H2 O molecules are linked by N–H· · · O and O–H· · · O bonds to form a host lattice featuring a system of parallel channels, which accommodate the guest Me4 N+ cations (see Section 20.4.4 for further details). The measured dimensions of the [BO(OH)2 ]− anion, which has crystallographically imposed symmetry m, show that the valence tautomeric form I with a formal B=O double bond makes a more important contribution than II to its electronic structure (Fig. 13.5.3). 13.5.2

Fig. 13.5.2.

Structure of layer of orthorhombic metaboric acid.

Structure of borates

(1) Structural units in borates The many structural components that occur in borates consist of planar triangular BO3 units and/or tetrahedral BO4 units with vertex-sharing linkage, and may be divided into three kinds. Some examples are given below: O HO

B–

O– OH

I B– Ο B– OH

132.3(5) pm 139.5(3) pm

HO

B

OH

II O – B–OH 124.3(2)° HO–B –OH 111.3(3)°

Fig. 13.5.3.

Valence-bond structural formulas for the dihydrogen borate ion, [BO(OH)2 ]− , and its measured dimensions in [(CH3 )4 N]+ [BO(OH)2 ]− · 2(NH2 )2 CO·H2 O.

488

Structural Chemistry of Selected Elements (a)

[BO3]3–

[(BO2)–]n

[B2O5]4–

[B3O6]3–

(b)

[BO4]5–

B(OH)4–

[B2O(OH)6]2–

[B2(O2)2(OH)4]2–

(c)

[B5O6(OH)4]–

[B3O3(OH)5]2–

[B4O5(OH)4]2–

Fig. 13.5.3.

Structural units in borates.

(a) Units containing B in planar BO3 coordination only [structures show in Fig. 13.5.3(a)]: BO33− : Mg3 (BO3 )2 , LaBO3 [B2 O5 ]4− : Mg2 B2 O5 , Fe2 B2 O5 [B3 O6 ]3− : K3 B3 O6 , Ba3 (B3 O6 )2 ≡ BaB2 O4 (BBO) [(BO2 )− ]n : Ca(BO2 )2 (b) Units containing B in tetrahedral BO4 coordination only [structure shown in Fig. 13.5.3(b)]: BO45− : TaBO4 B(OH)4− : Na2 [B(OH)4 Cl] [B2 O(OH)6 ]2− : Mg[B2 O(OH)6 ] [B2 (O2 )2 (OH)4 ]2− : Na2 [B2 (O2 )2 (OH)4 ]·6H2 O (c) Units containing B in both BO3 and BO4 coordination [Structure shown in Fig. 13.5.3(c)]: [B5 O6 (OH)4 ]− : K[B5 O6 (OH)4 ]·2H2 O [B3 O3 (OH)5 ]2− : Ca[B3 O3 (OH)5 ]·H2 O [B4 O5 (OH)4 )2− : Na2 [B4 O5 (OH)4 ]·8H2 O

Group 13 Elements (a) 146.4

489

(b) 143.9 137.1 137.4 136.3

150.0

148.5

(c) Fig. 13.5.4.

Structure of borax: (a) bond lengths in [B4 O5 (OH)4 ]2− (in pm), (b) perspective view of the anion, and (c) [B4 O5 (OH)2− 4 ]n chain.

(2) Structure of borax The main source of boron comes from borax, which is used in the manufacture of borosilicate glass, borate fertilizers, borate-based detergents, and flame-retardants. The crystal structure of borax was determined by Xray diffraction in 1956, and by neutron diffraction in 1978. It consists of + B4 O5 (OH)2− 4 , Na ions, and water molecules, so that its chemical formula is Na2 [B4 O5 (OH)4 ]·8H2 O, not Na2 B4 O7 ·10H2 O as given in many older books. The structure of [B4 O5 (OH)4 ]2− is shown in Figs. 13.5.4(a) and (b). In the crystal, the anions are linked by O–H· · · O hydrogen bonds to form an infinite chain, as shown in Fig. 13.5.4(c). The sodium ions are octahedrally coordinated by water molecules, and the octahedra share edges to form another chain. These two kinds of chains are linked by weaker hydrogen bonds between the OH groups of [B4 O5 (OH)4 ]2− anions and the aqua ligands, and this accounts for the softness of borax. (3) Structural principles for borates Several general principles have been formulated in connection with the structural chemistry of borates: (a) In borates, boron combines with oxygen either in trigonal planar or tetrahe5− dral coordination. In addition to the mononuclear anions BO3− 3 and BO4 and their partially or fully protonated forms, there exists an extensive series of polynuclear anions formed by corner-sharing of BO3 and BO4 units. The polyanions may form separate boron–oxygen complexes, rings, chains, layers, and frameworks. (b) In boron–oxygen polynuclear anions, most of the oxygen atoms are linked to one or two boron atoms, and a few can bridge three boron atoms. (c) In borates, the hydrogen atoms do not attach to boron atoms directly, but always to oxygens not shared by two borons, thereby generating OH groups. (d) Most boron–oxygen rings are six-membered, comprising three B atoms and three oxygen atoms. (e) In a borate crystal there may be two or more different boron–oxygen units.

490

Structural Chemistry of Selected Elements 13.6

Organometallic compounds of group 13 elements

13.6.1

Compounds with bridged structure

The compounds Al2 (CH3 )6 , (CH3 )2Al(µ-C6 H5 )2Al(CH3 )2 , and (C6 H5 )2Al(µC6 H5 )2Al(C6 H5 )2 all have bridged structures, as shown in Figs. 13.6.1 (a), (b) and (c) respectively. The bond distances and angles are listed in Table 13.6.1. The bonding in the Al–C–Al bridges involves a 3c-2e molecular orbital formed from essentially sp3 orbitals of the C and Al atoms. This type of 3c-2e interaction in the bridge necessarily results in an acute Al–C–Al angle (75◦ to 78◦ ), which is consistent with the experimental data. This orientation is sterically favored and places each ipso-carbon atom in an approximately tetrahedral configuration. In the structure of Me2 Ga(µ–C≡C–Ph)2 GaMe2 [Fig. 13.6.1(d)], each alkynyl bridge leans over toward one of the Ga centers. The organic ligand

(a)

(b)

(c)

Al

Al

(d)

Al

(e)

In Ga

Fig. 13.6.1.

Structure of some group 13 organometallic compounds: (a) Al2 (Me)6 , (b) Al2 (Me)4 (Ph)2 , (c) Al2 (Ph)6 , (d) Ga2 Me4 (C2 Ph)2 , and (e) In(Me)3 tetramer. Table 13.6.1. Structural parameters found in some carbon-bridged organoaluminum compounds

Compound

Al2 Me6 Al2 Me4 Ph2 Al2 Ph6

Angle (◦ )

Distance (pm) Al–Cb

Al–Ct

Al · · · Al

Al–C–Al

C–Al–C (internal)

214 214 218

197 197 196

260 269 270

74.7 77.5 76.5

105.3 101.3 103.5

C–Al–C (external) 123.1 115.4 121.5

Group 13 Elements

491

forms an Ga–C σ bond and interacts with the second Ga center by using its C≡C π bond. Thus each alkynyl group is able to provide three electrons for bridge bonding, in contrast to one electron as normally supplied by an alkyl or aryl group. Compounds In(Me)3 and Tl(Me)3 are monomeric in solution and the gas phase. In the solid state, they also exist as monomers essentially, but close intermolecular contacts become important. In crystalline In(Me)3 , significant In· · ·C intermolecular interactions are observed, suggesting that the structure can be described in terms of cyclic tetramers, as shown in Fig. 13.6.1(e), with interatomic distances of In–C 218 pm and In· · ·C 308 pm. The corresponding bond distances in isostructural Tl(Me)3 are Tl–C = 230 pm and Tl· · · C = 316 pm. 13.6.2

Compounds with π bonding

Many organometallic compounds of group 13 are formed by π bonds. The π ligands commonly used are olefins, cyclopentadiene, or their derivatives. The structure of the dimer [ClAl(Me–C=C–Me)AlCl]2 is of interest. There are 3c-2e π bonds between the Al atoms and the C=C bonds, as shown in Fig. 13.6.2(a). The Al–C distances in the Al-olefin units are relatively long, approximately 235 pm, but the sum of the four interactions lead to remarkable stability of the dimer. The energy gained through each Al–olefin interaction is calculated to be about 25 to 40 kJ mol−1 . The [Al(η5 -Cp*)2 ]+ (Cp* = C5 Me5 ) ion is at present the smallest sandwich metallocene of any main-group element. The Al–C bond length is 215.5 pm. Figure 13.6.2(b) shows the structure of this ion. The molecular structure of Al4 Cp∗4 in the crystal is shown in Fig. 13.6.2(c). The central Al4 tetrahedron has Al–Al bond length 276.9 pm, which is shorter

(a)

(b)

(c)

A1

A1

A1 Cl

(d)

(e)

(f)

Ga

In

Fig. 13.6.2.

Structure of some organometallic compounds formed by π bonds: (a) [ClAl(Me–C=C–Me)AlCl]2 , (b) [Al(Cp∗ )2 ]+ , (c) Al4 Cp∗4 , (d) GaCp∗ , and (e) InCp(or TlCp).

492

Structural Chemistry of Selected Elements than those in Al metal (286 pm). Each Cp∗ ring is η5 -coordinated to an Al atom, whereby the planes of the Cp∗ rings are parallel to the opposite base of the tetrahedron. The average Al–C distances is 233.4 pm. The half-sandwich structure of GaCp∗ in the gas phase, as determined by electron diffraction, is shown in Fig. 13.6.2(d). This compound has a pentagonal pyramidal structure with an η5 -C5 ring. The Ga–C distance is 240.5 pm. Both CpIn and CpTl are monomeric in the gas phase, but in the solid they possess a polymeric zigzag chain structure, in which the In (or Tl) atoms and Cp rings alternate, as shown in Fig. 13.6.2(e). 13.6.3

Compounds containing M–M bonds

The compounds R2Al–AlR2 , R2 Ga–GaR2 , and R2 In–InR2 [R=CH(SiMe3 )2 ] have been prepared and characterized. The bond lengths in these compounds are Al–Al 266.0 pm, Ga–Ga 254.1 pm, and In–In 282.8 pm; the M2 C4 frameworks are planar as shown in Fig. 13.6.3(a). In Al2 (C6 H2 i Pr3 )4 , Ga2 (C6 H2 i Pr3 )4 , and In2 [C6 H2 (CF3 )3 ]4 , the bond lengths are Al–Al 265 pm, Ga–Ga 251.5 pm, and In–In 274.4 pm, and here the M2 C4 framework are nonplanar, as shown in Fig. 13.6.3(b). In these structures the Ga–Ga bond lengths are shorter than the Al–Al bond lengths. The anomalous behavior of gallium among Group 13 elements is due to the insertion of electrons into the d orbitals of the preceding 3d elements in the Periodic Table and the associated contraction of the atomic radius. K (a)

(b)

(c)

Ga

(d)

(e)

Ga

(f)

Al

Al

SiMe3 Fig. 13.6.3.

Structures of some compounds containing M–M bonds: (a) planar M2 R4 (M = Al, Ga, In), (b) nonplanar M2 R4 (M = Al, Ga, In), (c) K2 Ga3 core of K2 [Ga3 (C6 H3 Mes2 )3 ], (d) [GaC(SiMe3 )3 ]4 , (e) (AlMe)8 (CCH2 Ph)5 (C≡C–Ph), and (f) icosahedral Al12 core in K2 [Al12i Bu12 ].

Group 13 Elements

493

The structures of compounds Na2 [Ga3 (C6 H3 Mes2 )3 ] and K2 [Ga3 (C6 H3 Mes2 )3 ] are worthy of note. In these compounds, the Na2 Ga3 and K2 Ga3 cores have trigonal bipyramidal geometry, as shown in Fig. 13.6.3(c). The bond lengths are Ga–Ga 244.1 pm (Na salt), 242.6 pm (K salt), Ga–Na 322.9 pm, and Ga–K 355.4 pm. The planarity of the Ga3 ring and the very short Ga–Ga bonds implies electron delocalization in the three-membered ring, the requisite two π electrons being provided by the two K (or Na) atoms (one electron each) to the empty pz orbitals of the three sp2 -hybridized Ga atoms. Figures 13.6.3(d)–(f) show the structures of three compounds which contain metallic polyhedral cores. In [GaC(SiMe3 )3 ]4 , the Ga–Ga bond length is 268.8 pm, in (AlMe)8 (CCH2 Ph)5 (C≡C–Ph) the Al–Al bond lengths are observed to be close to two average values: 260.9 and 282.9 pm, and in K2 [Al12i Bu12 ] the Al–Al bond length is 268.5 pm. Al50 Cp∗12 (or Al50 C120 H180 ) is a giant molecule, whose crystal structure shows a distorted square-antiprismatic Al8 moiety at its center, as shown in Fig. 13.6.4. This Al8 core is surrounded by 30 Al atoms that form an icosidodecahedron with 12 pentagonal faces and 20 trigonal faces. Each pentagonal faces is capped by an AlCp* unit, and the set of 12 Al atoms forms a very regular icosahedron, in which the Al· · ·Al average distance is 570.2 pm. Each of the peripheral 12 Al atoms is coordinated by 10 atoms (5 Al and 5 C) in the form of a staggered “mixed sandwich.” In the molecule, the average Al–Al bond length is 277.0 pm (257.8–287.7 pm). The 60 CH3 groups of the 12 Cp∗ ligands at the surface exhibits a topology resembling that of the carbon atoms in fullerene-C60 . The average distance between a pair of nearest methyl groups of neighboring Cp* ligands (386 pm) is approximately twice the van der Waals radius of a methyl group (195 pm). The entire Al50 Cp*12 molecule has a volume which is about five times large than that of a C60 molecule.

Fig. 13.6.4.

Molecular structure of Al50 Cp∗12 (Cp∗ = pentamethylcyclopentadienide). For clarity, the Cp∗ units are omitted, and only the bonds from the outer 12 Al atoms toward the ring centers are shown. The shaded atoms represent the central distorted square-antiprismatic Al8 moiety.

494

Structural Chemistry of Selected Elements (a)

(b) PEt3

I Ga

I I

Ga PEt3

N

I

N

In

I Ga

(c)

InR2

R2In

PEt3

InR2

R = 2,4,6-iPr3C6H2

N

N

In

In

N In N N In I

N

N

N In

N

N

N In N

_

= Ar

N

N

Ar

Ar = 2,6-iPr2C6H3

I

Fig. 13.6.5.

Structural formulas of some open-chain homocatenated compounds of heavier group 13 elements.

13.6.4

Linear catenation in heavier group 13 elements

For the heavier congeners of boron, the occurrence of well-characterized compounds possessing a linear extended skeleton containing two or more unsupported two-electron E–E bonds is quite rare. Some discrete molecules exhibiting this feature include the open-chain trigallium subhalide complex I2 (PEt3 )Ga–GaI(PEt3 )–GaI2 (PEt3 ) (Fig. 13.6.5(a)) and the trigonal tetranuclear indium complex {In[In(2,4,6-i Pr3 C6 H2 )2 ]3 } (Fig. 13.6.5(b)). Using a chelating ligand of the β-diketiminate class, a novel linear homocatenated hexanuclear indium compound has been synthesized (Fig. 13.6.5(c)). The four internal indium atoms are in the +1 oxidation state, and the terminal indium atoms, each carrying an iodo ligand, are both divalent. The coordination geometry at each indium center is distorted tetrahedral. As shown in Fig. 13.6.6, the mixed-valent molecule has a pseudo C2 axis with a β-diketiminate ligand chelated to each metal center, and its zigzag backbone is held together by five unsupported In–In single bonds constructed from sp3 hybrid orbitals.

Fig. 13.6.6.

N(1)

Molecular structure of a linear homocatenated compound containing six indium centers. The 3,5-dimethylphenyl groups of the β-diketiminate ligands have been omitted for clarity. Bond lengths (pm): In(1)–In(2) 281.2, In(2)–In(3) 283.5, In(3)–In(4) 285.4, In(4)–In(5) 284.1, In(5)–In(6) 282.2; In(1)–I(1) 279.8, In(6)–I(2) 278.0; standard deviation 0.1 pm. Average In–In–In bond angle at In(2) to In(5) is 139.4◦ .

I(1)

N(6)

N(10) N(9)

In(3)

N(7) In(5)

In(1) In(2) N(5)

N(2) N(3)

N(4)

In(4)

N(12) In(6)

N(8) I(2)

13.7

N(11)

Structure of naked anionic metalloid clusters

The term metalloid cluster is used to describe a multinuclear molecular species in which the metal atoms exhibit closest packing (and hence delocalized intermetallic interactions) like that in bulk metal, and the metal–metal contacts outnumber the peripheral metal–ligand contacts. Most examples are found in the field of precious-metal cluster chemistry. In recent years, an increasing number of cluster species of group 13 elements have been synthesized with cores

Group 13 Elements

495

(b)

(d) (a) Fig. 13.7.1.

Structure of Ga84 [N(SiMe3 )2 ]20 4− [the larger circles (shaded and unshaded) represent Ga atom, and the small circles represent N atoms]: (a) central Ga2 unit, (b) Ga32 shell, (c) a “belt” of 30 Ga atoms, and (d) the front of Ga84 [N(SiMe3 )2 ]20 4−. The Ga2 and N atoms at the back are not shown, the Ga32 shell is emphasized by the broken lines, the “belt” of 30 Ga atoms are shaded, and for the ligands N(SiMe3 )2 only the N atoms directly bonded to the Ga atoms are shown.

(c)

consisting of Aln (n = 7, 12, 14, 50, 69) and Gam (m = 9, 10, 19, 22, 24, 26, 84) atoms, for example [Al77 {N(SiMe3 )2 }20 ]2− and [Ga84 {N(SiMe3 )2 }20 ]4− . 13.7.1

Structure of Ga84 [N(SiMe3 )2 ]204−

The largest metalloid cluster characterized to date is Ga84 [N(SiMe3 )2 ]4− 20 , the structure of which is illustrated in Fig. 13.7.1. It comprises four parts: a Ga2 unit, a Ga32 shell, a Ga30 “belt,” and 20 Ga[N(SiMe3 )2 ] groups. The Ga2 unit [as shown in (a)] is located at the center of the 64 naked Ga atoms; the Ga–Ga bond distance is 235 pm, which is almost as short as the “normal” triple Ga–Ga bond (232 pm). The Ga2 unit is encapsulated by a Ga32 shell in the form of a football with icosahedral caps, as shown in (b). The Ga2 @Ga32 aggregate is surrounded by a belt of 30 Ga atoms that are also naked, as shown in (c). Finally the entire Ga64 framework is protected by 20 Ga[N(SiMe3 )2 ] groups to form Ga84 [N(SiMe3 )2 ]204− , as shown in (d). This large anionic cluster has a diameter of nearly 2 nm. 13.7.2

Structure of NaTl

The structure of sodium thallide NaTl can be understood as a diamond-like framework of Tl atoms, whose vacant sites are completely filled with Na atoms. Figure 13.7.2(a) shows the structure of NaTl, in which the Tl–Tl covalent bonds are represented by solid lines. The Tl atom has three valence electrons, which are insufficient for the construction of a stable diamond framework. The deficit can be partially compensated by the introduction of Na atoms. The effective radius of the Na atom is considerably smaller than that in pure metallic sodium.

496

Structural Chemistry of Selected Elements

Si Na

Li

Tl Fig. 13.7.2.

(a)

Structure of (a) NaTl and (b) Li2AlSi.

Al (b)

Therefore, the chemical bonding in NaTl is expected to be a mixture of covalent, ionic, and metallic interactions. The NaTl-type structure is the prototype for Zintl phases, which are intermetallic compounds which crystallize in typical “non-metal” crystal structures. Binary AB compounds LiAl, LiGa, LiIn and NaIn are both isoelectronic (isovalent) and isostructural with NaTl. In the Li2AlSi ternary compound, Al and Si form a diamond-like framework, in which the octahedral vacant sites of the Al sublattice are filled by Li atoms, as shown in Fig. 13.7.2(b). From the crystal structure, physical measurements, and theoretical calculations, the nature of the chemical bond in the NaTl-type compound AB can be understood in the following terms: (a) Strong covalent bonds exist between the B atoms (Al, Ga, In, Tl, Si). (b) The alkali atoms (A) are not in bonding contact. (c) The chemical bond between the A and B framework is metallic with a small ionic component. (d) For the upper valence/conduction electron states a partial metal-like charge distribution can be identified.

13.7.3

Naked Tlm− n anion clusters

The heavier elements of Group 13, in particular thallium, are able to form discrete naked clusters with alkali metals. Table 13.7.1 lists some examples of Tlm− n naked anion clusters, and Fig. 13.7.3 shows their structures. The bonding in these Tlnm− anion clusters is similar to that in boranes. For example, the bond valences (b) of Tl57− and centered Tl1311− clusters are equal to those of B5 H52− and B12 H122− , respectively. Note that, in Tl1311− , the central Tl atom contributes all three valence electrons to cluster bonding, so that the total number of bonding electrons is (3 + 12 × 1 + 11) = 26. This cluster is thus consolidated by ten Tl–Tl–Tl 3c-2e and three Tl–Tl 2c-2e bonds. The Tl99− cluster has 36 valence electrons, and its bond valence b is 18. The cluster is stabilized by three Tl–Tl–Tl 3c-2e bonds, as labeled by the three shaded faces in Fig. 13.7.3(e), and the remaining twelve edges represent 12 Tl–Tl 2c-2e bonds.

Group 13 Elements

497

m− Table 13.7.1. Some examples of Tln anion clusters

Composition Anion

Structure in Cluster Fig. 13.7.3 symmetry

Bond Bonding valence (b)

Na2 Tl

Tl48−

(a)

Td

6

Na2 K21 Tl19

2Tl57−

(b)

D3h

9

Tl99−

(e)

defective Ih

18

KTl

Tl66−

(c)

D4h

12

K10 Tl7

Tl77− , 3e−

(d)

∼ D5h

14

K8 Tl11

Tl117− , e−

(f)

∼ D3h

24

Na3 K8 Tl13

Tl1311−

(g)

Centered ∼ Ih

23

D 6 Tl–Tl 2c-2e bonds 3Tl–Tl–Tl 3c-2e bonds 3Tl–Tl 2c-2e bonds D 3Tl–Tl–Tl 3c-2e bonds 12Tl–Tl 2c-2e bonds D 12 Tl–Tl 2c-2e bonds 5Tl–Tl–Tl 3c-2e bonds 4Tl–Tl 2c-2e bonds D 3Tl–Tl–Tl 3c-2e bonds 18Tl–Tl 2c-2e bonds D 10Tl–Tl–Tl 3c-2e bonds 3Tl–Tl 2c-2e bonds

The compound K10 Tl7 is composed of ten K+ , a Tl77− and three delocalized electrons per formula unit and exhibits metallic properties. The Tl77− cluster is an axially compressed pentagonal bipyramid conforming closely to D5h symmetry [Fig. 13.7.3(d)]. The apex–apex bond distance of 346.2 pm is slightly longer than the bonds in the pentagonal waist (318.3–324.7 pm). Comparison between the structures of Tl77− and B7 H72− [Fig. 13.4.6(a)] shows that both are pentagonal bipyramidal but Tl77− is compressed along the C5 axis for the formation of a coaxial 2c-2e Tl–Tl bond, so the bond valences of Tl77− and B7 H72− are 14 and 13, respectively.

(a)

(b)

(c)

(d)

Fig. 13.7.3.

Structures of some Tlnm− anion clusters: (a) Tl48− , (b) Tl57− , (c) Tl66− , (d) Tl77− ,

(e) Tl99− (shaded faces represent three

(e)

(f)

(g)

Tl–Tl–Tl 3c-2e bonds), (f) Tl117− , (g) Tl1311− .

498

Structural Chemistry of Selected Elements References 1. N. N. Greenwood and A. Earnshaw, Chemistry of the Elements, 2nd edn., Butterworth Heinemann, Oxford, 1997. 2. C. E. Housecroft and A. G. Sharpe, Inorganic Chemistry, 2nd edn., Prentice-Hall, London, 2004. 3. D. F. Shriver, P. W. Atkins, T. L. Overton, J. P. Rourke, M. T. Weller and F. A. Armstrong, Inorganic Chemistry, 4th edn., Oxford University Press, Oxford, 2006. 4. D. M. P. Mingos, Essential Trends in Inorganic Chemistry, Oxford University Press, Oxford, 1998. 5. G. E. Rodgers, Introduction to Coordination, Solid State, and Descriptive Inorganic Chemistry, McGraw-Hill, New York, 1994. 6. G. Meyer, D. Naumann and L. Wesemann (eds.), Inorganic Chemistry Highlights, Wiley–VCH, Weinheim, 2002. 7. C. E. Housecroft, Boranes and Metallaboranes: Structure, Bonding and Reactivity, 2nd edn., Ellis Horwood, New York, 1994. 8. C. E. Housecroft, Cluster Molecules of the p-Block Elements, Oxford University Press, Oxford, 1994. 9. D. M. P. Mingos and D. J. Wales, Introduction to Cluster Chemistry, Prentice-Hall Englewood Cliffs, NJ, 1990. 10. W. Siebert (ed.), Advances in Boron Chemistry, Royal Society of Chemistry, Cambridge, 1997. 11. G. A. Olah, K. Wade and R. E. Williams (eds.), Electron Deficient Boron and Carbon Clusters, Wiley, New York, 1991. 12. M. Driess and H. Nöth (eds.), Molecular Clusters of the Main Group Elements, Wiley–VCH, Weinheim, 2004. 13. R. A. Beaudet, “The molecular structures of boranes and carboranes,” in J.F. Liebman, A. Greenberg and R. E. Williams (eds.), Advances in Boron and the Boranes, VCH, New York, 1988. 14. W. Siebert (ed.), Advances in Boron Chemistry, Royal Society of Chemistry, Cambridge, 1997. 15. I. D. Brown, The Chemical Bond in Inorganic Chemistry: The Bond Valence Model, Oxford University Press, New York, 2002. 16. U. Müller, Inorganic Structural Chemistry, 2nd edn., Wiley, Chichester, 2006. 17. T. C. W. Mak and G.-D. Zhou, Crystallography in Modern Chemistry: A Resource Book of Crystal Structures, Wiley–Interscience, New York, 1992. 18. E. Abel, F. G. A. Stone and G. Wilkinson (eds.), Comprehensive Organometallic Chemistry II, Vol. 1, Pergamon Press, Oxford, 1995. 19. S. M. Kauzlarich (ed.), Chemistry, Structure, and Bonding of Zintl Phases and Ions, VCH, New York, 1996. 20. G. D. Zhou, Bond valence and molecular geometry. University Chemistry (in Chinese), 11, 9–18 (1996). 21. T. Peymann, C. B. Knobler, S. I. Khan and M. F. Hawthorne, Dodeca(benzyloxy)dodecaborane B12 (OCH2 Ph)12 : A stable derivative of hypercloso-B12 H12 . Angew. Chem. Int. Ed. 40, 1664–7 (2001). 22. E. D. Jemmis, M. M. Balakrishnarajan and P. D. Pancharatna, Electronic requirements for macropolyhedral boranes. Chem. Rev. 102, 93–144 (2002). 23. Z. Xie, Advances in the chemistry of metallacarboranes of f -block elements. Coord. Chem. Rev. 231, 23–46 (2002). 24. J. Vollet, J. R. Hartig and H. Schnöckel, Al50 C120 H180 : A pseudofullerene shell of 60 carbon atoms and 60 methyl groups protecting a cluster core of 50 aluminium atoms. Angew. Chem. Int. Ed. 43, 3186-9 (2004).

Group 13 Elements 25. H. W. Roesky and S. S. Kumar, Chemistry of aluminium(I). Chem. Commun. 4027– 38 (2005). 26. C. Dohmeier, D. Loos and H. Schnöckel, Aluminum(I) and gallium(I) compounds: syntheses, structures, and reactions. Angew. Chem. Int. Ed. 35, 129–49 (1996). 27. A. Schnepf and H. Schnöckel, Metalloid aluminum and gallium clusters: element modifications on the molecular scale?. Angew. Chem. Int. Ed. 41, 3532–52 (2002). 28. W. Uhl, Organoelement compounds possessing Al–Al, Ga–Ga, In–In, and Tl–Tl single bonds. Adv. Organomet. Chem. 51, 53–108 (2004). 29. S. Kaskel and J. D. Corbett, Synthesis and structure of K10 Tl7 : the first binary trielide containing naked pentagonal bipyramidal Tl7 clusters. Inorg. Chem. 39, 778–82 (2000). 30. M. S. Hill, P. B. Hitchcock and R. Pongtavornpinyo, A linear homocatenated compound containing six indium centers. Science 311, 1904–7 (2006).

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14

Structural Chemistry of Group 14 Elements

14.1

Allotropic modifications of carbon

With the exception of the gaseous low-carbon molecules: C1 , C2 , C3 , C4 , C5 , . . ., the carbon element exists in the diamond, graphite, fullerene, and amorphous allotropic forms. 14.1.1

Diamond

Diamond forms beautiful, transparent, and highly refractive crystals, and has been used as a noble gem since antiquity. It consists of a three-dimensional network of carbon atoms, each of which is bonded tetrahedrally by covalent C–C single bonds to four others, so that the whole diamond crystal is essentially a “giant molecule.” Nearly all naturally occurring diamonds exist in the cubic ¯ (no. 227), with a = 356.688 pm and Z = 8. The C–C form, space group Fd3m bond length is 154.45 pm, and the C–C–C bond angle is 109.47◦ . In the crystal structure, the carbon atoms form six-membered rings that take the all-chair conformation [Fig. 14.1.1(a)]. The mid-point of every C–C bond is located at an inversion center, so that the six nearest carbon atoms about it are in a staggered arrangement, which is the most stable conformation. In addition to cubic diamond, there is a metastable hexagonal form, which has been found in aerorite and can be prepared from graphite at 13 GPa above 1300 K. Hexagonal diamond crystallizes in space group P63 /mmc (no. 194) with a = 251 pm, c = 412 pm and Z = 4, as shown in Fig. 14.1.1(b). The bond type and the C–C bond length are the same as in cubic diamond. The difference between the two forms is the orientation of two sets of tetrahedral bonds about neighboring carbon atoms: cubic diamond has the staggered arrangement

(a)

Fig. 14.1.1.

Crystal structure of diamond: (a) cubic form and (b) hexagonal form.

(b)

Group 14 Elements

501

about each C–C bond at an inversion center, but in hexagonal diamond some bonds take the eclipsed arrangement related by mirror symmetry. As repulsion between nonbonded atoms in the eclipsed arrangement is greater than that in the staggered arrangement, hexagonal diamond is much rarer than cubic diamond. Diamond is the hardest natural solid known and has the highest melting point, 4400 ± 100 K (12.4 GPa). It is an insulator in its pure form. Since the density of diamond (3.51 g cm−3 ) far exceeds that of graphite (2.27 g cm−3 ), high pressures can be used to convert graphite into diamond even though graphite is thermodynamically more stable by 2.9 kJ mol−1 . To attain commercially viable rates for the pressure-induced conversion of graphite to diamond, a transitionmetal catalyst such as iron, nickel, or chromium is generally used. Recently, the method has been employed to deposit thin films of diamond onto a metallic or other material surface. The extreme hardness and high thermal conductivity of diamond find applications in numerous areas, notably the hardening of surfaces of electronic devices and as cutting and/or grinding materials. Elemental silicon, germanium, and tin have the cubic diamond structure with unit-cell edge a = 543.072, 565.754, and 649.12 pm (α-Sn), respectively. 14.1.2

Graphite

Graphite is the common modification of carbon that is stable under normal conditions. Its crystal structure consists of planar layers of hexagonal carbon rings. Within the layer each carbon atom is bonded covalently to three neighboring carbon atoms at 141.8 pm. The σ bonds between neighbors within a layer are formed from the overlap of sp2 hybrids, and overlap involving the remaining electron and perpendicular pz orbital on every atom generates a network of π bonds that are delocalized over the entire layer. The relatively free movement of π electrons in the layers leads to abnormally high electrical conductivity for a non-metallic substance. The layers are stacked in a staggered manner with half of the atoms of one layer situated exactly above atoms of the layer below, and the other half over the rings centers. There are two crystalline forms that differ in the sequence of layer stacking. (1) Hexagonal graphite or α-graphite: The layers are arranged in the sequence …ABAB…, as shown in Fig. 14.1.2(a). The space group is P63 /mmc (a)

(b)

Fig. 14.1.2.

Structure of graphite: (a) α-graphite and (b) β-graphite.

502

Structural Chemistry of Selected Elements (no. 194), and the unit cell has dimensions of a = 245.6 pm and c = 669.4 pm, so that the interlayer distance is c/2 = 334.7 pm. (2) Rhombohedral graphite or β-graphite: The layers are arranged in the sequence …ABCABC…, as shown in Fig. 14.1.2(b). The space group ¯ (no. 166), and the unit cell has dimensions of a = 246.1 pm and is R3m c = 1006.4 pm. The interlayer separation c/3 = 335.5 pm is similar to that of α-graphite. The enthalpy difference between hexagonal and rhombohedral graphite is only 0.59 ± 0.17 kJ mol−1 . The two forms are interconvertible by grinding (hexagonal → rhombohedral) or heating above 1025 ◦ C (rhombohedral → hexagonal). Partial conversion leads to an increase in the average spacing between layers; this reaches a maximum of 344 pm for turbostratic graphite in which the stacking sequence of the parallel layers is completely random. In graphite the layers are held together by van der Waals forces. The relative weak binding between layers is consistent with its softness and lubricity, as adjacent layers are able to easily slide by each other. Graphite mixed with clay constitutes pencil “lead,” which should not be confused with metallic lead or dark-gray lead sulfide. 14.1.3

Fullerenes

The third allotropic modification of carbon, the fullerenes, consists of a series of discrete molecules of closed cage structure bounded by planar faces, whose vertices are made up of carbon atoms. If the molecular cage consists of pentagons and hexagons only, the number of pentagons must always be equal to 12, while the number of hexagons may vary. Fullerenes are discrete globular molecules that are soluble in organic solvents, and their structure and properties are different from those of diamond and graphite. Fullerenes can be obtained by passing an electric arc between two graphite electrodes in a controlled atmosphere of helium, or by controlling the helium/oxygen ratio in the incomplete combustion of benzene, followed by evaporation of the carbon vapor and re-crystallization from benzene. The main product of the preparation is fullerene-C60 , and the next abundant product is fullerene-C70. The structure of C60 has been determined by single-crystal neutron diffraction and electron diffraction in the gas phase. It has icosahedral (Ih ) symmetry with 60 vertices, 90 edges, 12 pentagons, and 20 hexagons. The C–C bond lengths are 139 pm for 6/6 bonds (fusion of two six-membered rings) and 144 pm for 6/5 bonds (fusion between five- and six-membered rings). The 60 carbon atoms all lie within a shell of mean diameter 700 pm. Figure 14.1.3(a) shows the soccerball shape of the C60 molecule. Each carbon atom forms three σ bonds with three neighbors, and the remaining orbitals and electrons of the 60 C atoms form delocalized π bonds. This structure may be formulated by the valencebond formula shown in Fig. 14.1.3(b). The C60 molecule can be chemically functionalized, and an unambiguous atom-numbering scheme is required for systematic nomenclature of its derivatives. Figure 14.1.3(c) shows the planar formula with carbon atom-numbering scheme of the C60 molecule. In the C60 molecule, the sum of the σ bond angles at each C atom is 348◦ (= 120◦ + 120◦ + 108◦ ), and the mean C–C–C angle is 116◦ . The π atomic orbital

Group 14 Elements (a)

(b)

503

(c)

Fig. 14.1.3.

Structure of fullerene-C60 : (a) molecular shape, (b) valence-bond formula, and (c) planar formula with carbon atom-numbering scheme.

lies normal to the convex surface, the angle between the σ and π orbitals being 101.64◦ . It may be approximately calculated that each σ orbital has s component 30.5% and p 69.5%, and each π orbital has s 8.5% and p 91.5%. Table 14.1.1. Some physical properties of fullerene-C60

Density (g cm−3 ) Bulk modulus (GPa) Refractive index (630 nm) Heat of combustion (crystalline C60 ) (kJ mol−1 ) Electron affinity (eV) First ionization energy (eV) Band gap (eV) Solubility (303 K) (g dm−3 ) CS2 Toluene Benzene CCl4 Hexane

1.65 18 2.2 2280 2.6–2.8 7.6 1.9 5.16 2.15 1.44 0.45 0.04

Fullerene-C60 is a brown-black crystal, in which the nearly spherical molecules rotate continuously at room temperature. The structure of the crystal can be considered as a stacking of spheres of diameter 1000 pm in cubic closest packing (a = 1420 pm) or hexagonal closest packing (a = 1002 pm, c = 1639 pm). Figure 14.1.4 shows the crystal structure of fullerene-C60 . Below 249 K, the molecules are orientated in an ordered fashion, and the symmetry of the crystal is reduced from a face-centered cubic lattice to a primitive cubic lattice. At 5 K, the crystal structure determined by neutron diffraction yielded the following data: space group Pa3¯ (no. 205), a = 1404.08(1) pm; C–C bond lengths: (6/6) 139.1 pm, (6/5) 144.4 pm, and 146.6 pm (mean 145.5 pm). In the C60 molecule, the mean distance from the center to every C vertex is 350 pm, so the molecule has a spherical skeleton with diameter 700 pm. Allowing for the van der Waals radius of the C atom (170 pm), the C60 molecule has a central cavity of diameter 360 pm, which can accommodate a foreign atom. Some physical properties of C60 are summarized in Table 14.1.1.

Fig. 14.1.4.

The cubic face-centered structure of fullerene-C60 .

504

Structural Chemistry of Selected Elements

(a) C20 (Ih)

(b) C50 (D5h)

(c) C70 (D5h)

Fig. 14.1.5.

Structures of some fullerenes. Note that (b) shows the carbon skeleton of C50 Cl10 , whose ten equatorial chloro substituents have been omitted.

(e) C78 (D3)

(d) C78 (C2v)

In addition to C60 , many other higher homologs have been prepared and characterized. Several synthetic routes to fullerenes have yielded gram quantities of pure C60 and C70 , whereas C76 , C78 , C80 , C82 , C84 and other fullerenes have been isolated as minor products. Figure 14.1.5 shows the structures of the following fullerenes: C20 , C50 , C70 , and two C78 -isomers. In general, the polyhedral closed cages of fullerenes are made up entirely of n three-coordinate carbon atoms that constitute 12 pentagonal and (n/2 − 10) hexagonal faces. The larger fullerenes synthesized so far do faithfully satisfy the isolated pentagon rule (IPR), which governs the stability of fullerenes comprising hexagons and exactly 12 pentagons. On the other hand, smaller fullerenes do not obey the IPR, and are so labile that their properties and reactivity have only been studied in the gas phase. The smallest fullerene that can exist theoretically is C20 . It has been synthesized from dodecahedrane C20 H20 by replacing the hydrogen atoms with relatively weakly bound bromine atoms to form a triene precursor of average composition [C20 HBr13 ], which was then subjected to debromination in the gas phase. The bowl isomer of C20 is likewise generated by gas-phase debromination of a [C20 HBr9 ] precursor prepared from bromination of corannulene C20 H10 . Identification of the two C20 isomers was achieved by mass-selective anion-photoelectron spectroscopy. Figure 14.1.5(a) shows the molecular structure of fullerene C20 . [C20HBr13] Dodecahedrane C20H20

Fullerene C20 [C20HBr9]

Corannulene C20H10

Bowl isomer of C20

[From H. Prinzbach, A. Weiler, P. Landenberger, F. Wahl, J. Worth, L. T. Scott, M. Gelmont, D. Olevano and B. v. Issendorff, Nature 407, 60–3 (2000).]

Group 14 Elements

505

Fullerene-C50 has been trapped as its perchloro adduct C50 Cl10 , which was obtained in milligram quantity from the addition of CCl4 to the usual graphite arc-discharge process for the synthesis of C60 and larger fullerenes. The D5h structure of C50 Cl10 , with all chlorine atoms lying in the equatorial plane and attached to sp3 carbon atoms, was established by mass spectrometry, 13 C NMR, and other spectroscopic methods. The idealized structure of C50 is displayed in Fig. 14.1.5(b). The fullerene-C70 molecule has D5h symmetry and an approximately ellipsoidal shape, as shown in Fig. 14.1.5(c). As in C60 , the 12 five-membered rings in C70 are not adjacent to one another. In contrast to C60 , C70 has an equatorial phenylene belt comprising 15 fused hexagons and two polar caps, each assembled from a pentagon that shares its edges with 5 hexagons. The curvature at the polar region is very similar to that of C60 . There are five sets of geometrically distinct carbon atoms, and the observed 13 C NMR signals have the intensity ratios of 1:1:2:2:1. The measured carbon–carbon bond lengths (Fig. 14.1.6) in the crystal structure of the complex (η2 -C70 )Ir(CO)Cl(PPh3 )2 suggest that two equivalent lowest-energy Kekulé structures per equatorial hexagon are required to describe the structure and reactivity properties of C70 .

ab

h g f e cd

a = 146.2 pm b = 142.3 c = 144.1 d = 143.2 e = 137.2 f = 145.3 g = 138.1 h = 146.3

Fig. 14.1.6.

Two equivalent valence bond structures of C70 and measured bond lengths of the polyhedral cage in (η2 -C70 )Ir(CO)Cl(PPh3 )2 .

The structures of two geometric isomers of fullerene-C78 have been elucidated by 13 C NMR spectroscopy: one has C2v symmetry, as shown in Fig. 14.1.5(d); the other has D3 symmetry, as shown in Fig. 14.1.5(e). Structural assignments with qualities ranging from reliable to absolutely certain have also been made for C74 (D3h ), C76 (D2 ), C78 , [a new isomer of C2v symmetry, which has a more spherical shape compared to the C78 (C2v ) isomer shown in Fig. 14.1.5(d)], C80 (D2 ), C82 (C2 ), C84 (D2 ), and C84 (D2d ). In addition to the single globular species, fullerenes can be formed by joining two or more carbon cages, as found for the dimer C120 shown in Fig. 14.1.7. Xray diffraction showed that the dimer is connected by a pair of C–C bonds linking the edges of hexagonal faces (6/6 bonds) in two C60 units to form a central fourmembered ring, in which the bond lengths are 157.5 pm (connecting the two cages) and 158.1 pm (6/6 bonds).

Fig. 14.1.7.

Molecular structure of the dimer [C60 ]2 .

506

Structural Chemistry of Selected Elements Fullerene-C60 was selected as ‘Molecule of the Year 1991’ by the journal Science (Washington). Discovery of this modification of carbon in the mid-1980s created a great excitement in the scientific community and popular press. Some of this interest undoubtedly stemmed from the fact that carbon is a common element that had been studied since ancient times, but still an entirely new field of fullerene chemistry suddenly emerged with great potential for exciting research and practical applications. 14.1.4

Amorphous carbon

Amorphous carbon is a general term that covers non-crystalline forms of carbon such as coal, coke, charcoal, carbon black (soot), activated carbon, vitreous carbon, glassy carbon, carbon fiber, carbon nanotubes, and carbon onions, which are important materials and widely used in industry. The arrangements of the carbon atoms in amorphous carbon are different from those in diamond, graphite, and fullerenes, but the bond types of carbon atoms are the same as in these three crystalline allotropes. Most forms of amorphous carbon consist of graphite scraps in irregularly packing. Coal is by far the world’s most abundant fossil fuel, with a total recoverable resource of about 1000 billion (1012 ) tons. It is a complex mixture of many compounds that contain a high percentage of carbon and hydrogen, but many other elements are also present as impurities. The composition of coal varies considerably depending on its age and location. A typical bituminous coal has the approximate composition 80% C, 5% H, 8% O, 3% S, and 2% N. The manifold structures of coal are very complex and not clearly defined. The high-temperature carbonization of coal yields coke, which is a soft, poorly graphitized form of carbon, most of which is used in steel manufacture. Activated carbon is a finely divided form of amorphous carbon manufactured from the carbonization of an organic precursor, which possesses a microporous structure with a large internal surface area. The ability of the hydrophobic surface to adsorb small molecules accounts for the widespread applications of activated carbon as gas filters, decoloring agents in the sugar industry, water purification agents, and heterogeneous catalysts. Carbon black (soot) is made by the incomplete combustion of liquid hydrocarbons or natural gas. The particle size of carbon black is exceedingly small, only 0.02 to 0.3 µm, and its principal application is in the rubber industry where it is used to strengthen and reinforce natural rubber. Carbon fibers are filaments consisting of non-graphitic carbon obtained by carbonization of natural or synthetic organic fibers, or fibers drawn from organic precursors such as resins or pitches, and subsequently heat-treated up to temperatures of about 300 ◦ C. Carbon fibers are light and exceeding strong, so that they are now important industrial materials that have gained increasing applications ranging from sport equipment to aerospace strategic uses. From observations in transmission electron micrography (TEM), carbon soot particles are found to have an idealized onion-like shelled structure, as shown in Fig. 14.1.8. Carbon onions varying from 3 to 1000 nm in diameter have been observed experimentally. In an idealized model of a carbon onion, the first shell is a C60 core of Ih symmetry, the second shell is C240 (comprising 22 × 60

Group 14 Elements

507

5 nm

Fig. 14.1.8.

Section of a carbon onion.

atoms), and in general the number of carbon atom in the nth shell is n2 × 60. The molecular formula of a carbon onion is C60 @C240 @C540 @C960 @. . ., and the intershell distance is always ∼350 pm. Recent work based on HRTEM (high-resolution transmission electron microscopy) and simulations has established that carbon onions are spherical rather than polyhedral, and the intershell spacing increases gradually from a value well below that of graphite at the center to the expected value at the outermost pair. The individual shells are not aligned in any regular fashion and do not rotate relative to each other. The innermost core can be a smaller fullerene (e.g. C28 ) or a diamond fragment varying in size from 2 to 4.5 nm, and the internal cavity can be as large as 2 nm in diameter.

14.1.5

Carbon nanotubes

Carbon nanotubes were discovered in 1991 and consist of elongated cages bounded by cylindrical walls constructed from rolled graphene (graphite-like) sheets. In contrast to the fullerenes, nanotubes possess a network of fused six-membered rings, and each terminal of the long tube is closed by a halffullerene cap. Single-walled carbon nanotubes (SWNTs) with diameters in the range 0.4 to 3.0 nm have been observed experimentally; most of them lie within the range 0.6 to 2.0 nm, and those with diameter 0.7, 0.5 and 0.4 nm correspond to the fullerenes C60 , C36 and C20 , respectively. Electron micrographs of the smallest 0.4 nm nanotubes prepared by the arc-discharge method showed that each is capped by half of a C20 dodecahedron and has an antichiral structure. A carbon SWNT can be visualized as a hollow cylinder formed by rolling a planar sheet of hexagonal graphite (unit-cell parameters a = 0.246, c = 0.669 nm). It can be uniquely described by a vector C = na1 + ma2 , where a1 and a2 are reference unit vectors as defined in Fig. 14.1.9. The SWNT is generated by rolling up the sheet such that the two end-points of the vector C are superimposed. The tube is denoted as (n, m) with n ≥ m, and its diameter D

508

Structural Chemistry of Selected Elements Armchair (m, m)

C

Chiral (8, 4)

a2 a1

Zigzag (n, 0)

O

Fig. 14.1.9.

Generation of the chiral (8,4) carbon nanotube by rolling a graphite sheet along the vector C = na1 + ma2 , and definition of the chiral angle θ . The reference unit vectors a1 and a2 are shown, and the broken lines indicate the directions for generating achiral zigzag and armchair nanotubes.

is given by 1

D = |C|/π = a(n2 + nm + m2 ) 2 /π The tubes with m = n are called “armchair” and those with m = 0 are referred to as “zigzag.” All others are chiral with the chiral angle θ defined as that between the vectors C and a1 ; θ can be calculated from the equation 1

θ = tan−1 [3 2 m/(m + 2n)].

armchair (5,5)

zigzag (9, 0) Fig. 14.1.10.

Lateral view of three kinds of carbon nanotubes with end caps: (a) armchair (5,5) capped by one-half of C60 , (b) zigzag (9,0) capped by one-half of C60 , and (c) an enantiomorphic pair of chiral SWNTs each capped by a hemisphere of icosahedral fullerene C140 .

chiral (15, –5)

chiral (10, 5)

The values of θ lies between 0◦ (for a zigzag tube) and 30◦ (for an armchair tube). Note that the mirror image of a chiral (n, m) nanotube is specified by (n + m, −m). The three types of SWNTs are illustrated in Fig. 14.1.10. There are multiwalled carbon nanotubes (MWNTs), each consisting of ten inner tubes or more. In a carbon MWNT, the spacing between two adjacent coaxial zigzag tubes (n1 , 0) and (n2 , 0) is 'd /2 = (0.123/π )(n2 − n1 ). However, this cannot be made to be close to c/2 = 0.335 nm (the interlayer separation

Group 14 Elements

509

Fig. 14.1.11.

A helical multi-walled carbon nanotube.

in graphite) by any reasonable combination of n2 and n1 , and hence no zigzag nanotube can exist as a component of a MWNT. On the other hand, a MWNT can be constructed for all armchair tubes (5m, 5m) with m = 1, 2, 3, etc., for which the intertube spacing is (0.123/π )31/2 (5) = 0.339 nm, which satisfies the requirement. In practice, defect-free coaxial nanotubes rarely occur in experimental preparations. The observed structures include the capped, bent, and toroidal SWNTs, as well as the capped and bent, branched, and helical MWNTs. Figure 14.1.11 shows the HRTEM micrograph of a helical multiwalled carbon nanotube which incorporates a small number of five- and seven-membered rings into the graphene sheets of the nanotube surfaces.

14.2

Compounds of carbon

More than twenty million compounds containing carbon atoms are now known, the majority of which are organic compounds that contain carbon–carbon bonds. From the perspective of structural chemistry, the modes of bonding, coordination, and the bond parameters of a particular element in its allotropic modifications may be further extended to its compounds. Thus organic compounds can be conveniently divided into three families that originate from their prototypes: aliphatic compounds from diamond, aromatic compounds from graphite, and fullerenic compounds from fullerenes. 14.2.1

Aliphatic compounds

Aliphatic compounds comprise hydrocarbons and their derivatives in which the molecular skeletons consist of tetrahedral carbon atoms connected by C–C single bonds. These tetrahedral carbon atoms can be arranged as chains, rings, or finite frameworks, and often with an array of functional groups as substituents on various sites. The alkanes Cn H2n+2 and their derivatives are typical examples of aliphatic compounds. Some frameworks of alicyclic compounds are derived from fragments of diamond, as shown in Fig. 14.2.1. In these molecules, all six-membered carbon rings have the chair conformation. Diamantane C14 H20 is also named

510

Structural Chemistry of Selected Elements

Adamantane, Td

Diamantane (congressane), D3d

Triamantane, C2v

Fig. 14.2.1.

Some frameworks of alicyclic compounds as fragments of diamond.

Isotetramantane, Cs

anti-Tetramantane, C2h

skew-Tetramantane, C2

congressane as it was chosen as the logo of the XIXth Conference of IUPAC in London in 1963 as a challenging target for the participants; the successful synthesis was accomplished two years later. There are three structural isomers of tetramantane C22 H28 . X-ray analysis of anti-tetramantane has revealed an interesting bond-length progression: CH–CH2 = 152.4 pm, C–CH2 = 152.8 pm, CH–CH = 153.7 pm, and C–CH = 154.2 pm, approaching the limit of 154.45 pm in diamond as the number of bonded H atoms decreases.

14.2.2

Aromatic compounds

Graphite typifies the basic structural unit present in aromatic compounds, in which the planar carbon skeletons of these molecules and their derivatives can be considered as fragments of graphite, each consisting of carbon atoms which use their sp2 hybrids to form σ bonds to one another, and overlap between the remaining parallel pz orbitals gives rise to delocalized π bonding. The aromatic compounds may be divided into the following four classes.

(1) Benzene and benzene derivatives Up to six hydrogen atoms in benzene can be mono- or poly-substituted by other atoms or groups to give a wide variety of derivatives. Up to six sterically bulky groups such as SiMe3 and ferrocenyl (C5 H5 FeC5 H4 , Fc) groups can be substituted into a benzene ring. Hexaferrocenylbenzene, C6 Fc6 , is of structural interest as a supercrowded arene, a metalated hexakis(cyclopentadienylidene)radialene, and the core for the construction of “Ferris wheel” supermolecules. In the crystalline solvate C6 Fc6 ·C6 H6 , the C6 Fc6 molecule adopts a propeller-like configuration with alternating up and down Fc groups around the central benzene ring. Perferrocenylation causes the benzene ring to take a chair conformation with alternating C–C–C–C dihedral angles of ±14◦ , and the elongated C–C bonds exhibit noticeable bond alternation averaging 142.7/141.1 pm. The Car –CFc bonds average 146.9(5) pm.

Group 14 Elements (a)

511 (b)

Azulene

Chrysene

Pentacene

Perylene Biphenylene

Pyrene

Triphenylene

Coronene

Acenaphthylene

Fig. 14.2.2.

Carbon skeletons of some polycyclic aromatic compounds of the (a) benzenoid type and (b) non-benzenoid type.

(2) Polycyclic benzenoid aromatic compounds These compounds consist of two or more benzene rings fused together, and the number of delocalized π electrons conforms to the Hückel (4n + 2) rule for aromaticity. Figure 14.2.2(a) shows the carbon skeletons of some typical examples. (3) Non-benzenoid aromatic compounds Many aromatic compounds have considerable resonance stabilization but do not possess a benzene nucleus, or in the case of a fused polycyclic system, the molecular skeleton contains at least one ring that is not a benzene ring. The + cyclopentadienyl anion C5 H− 5 , the cycloheptatrienyl cation C7 H7 , the aromatic annulenes (except for [6]annulene, which is benzene), azulene, biphenylene and acenaphthylene (see Fig. 14.2.2(b)) are common examples of non-benzenoid aromatic hydrocarbons. The cyclic oxocarbon dianions Cn O2− n (n = 3, 4, 5, 6) constitute a class of non-benzenoid aromatic compounds stabilized by two delocalized π electrons. Further details are given in Section 20.4.4. (4) Heterocyclic aromatic compounds In many cyclic aromatic compounds an element other than carbon (commonly N, O, or S) is also present in the ring. These compounds are called heterocycles. Figure 14.2.3 shows some nitrogen heterocycles commonly used as ligands, as well as planar, sunflower-like octathio[8]circulene, C16 S8 , which can be regarded as a novel form of carbon sulfide. 14.2.3

Fullerenic compounds

The derivatives of fullerenes are called fullerenic compounds, which are now mainly prepared from C60 and, to a lesser extent, from C70 and C84 . Since efficient methods for the synthesis and purification of gram quantities of C60 and C70 became available in the early 1990s, fullerene chemistry has developed at a phenomenal pace. There are many reactions which can generate

512

Structural Chemistry of Selected Elements (a)

(c)

(b)

(d)

(e) N

Fig. 14.2.3.

Some commonly used heterocyclic nitrogen ligands: (a) pyrazole, (b) imidazole, (c) pyridine-2-thiol, (d) pyrazine, (e) 4,4’-bipyridine, (f) quinoline, (g) 4,4’-bipyrimidine, (h) 1,8-naphthyridine, (i) 1,10-phenanthroline. Compounds (a), (b), and (c) occur in metal complexes in the anionic (deprontonated) form with delocalization of the negative charge. (j) Octathio[8]circulene has a highly symmetric planar structure.

N

N H

N

N

N

H N

(f)

SH

N

(g)

(j) S

N

N N

N (h)

S

N

OH

S

N

epoxides O

fullerols (OH)n

Hn

O2, hv

Xn

H2

X2

nuc

leop add hilic ition R

fullerene radicals

E

The principal reactions of C60 .

•

host–guest host complexes

t

C60

M M

M+

halofullerenes

hos

Rn

heterfullerenes

S S

fullerene derivatives Rn

M+ metal fullerides

S

S

N

fullerene amines RHN

S

N

(i)

fulleranes

Fig. 14.2.4.

N

MLn

calix[n]arene oligoorAgNO3 meri zatio cy n clo ad di t MLn ion

supramolecular assemblies

n fullerene oligomers

n– O

M endohedral metallofullerenes M@C60

M O M

fullerene cycloadducts

coordinaton compounds

organometallics

fullerenic compounds, as shown in Fig. 14.2.4. Unlike the aromatics, fullerenes have no hydrogen atoms or other groups attached, and so are unable to undergo substitution reactions. However, the globular fullerene carbon skeleton gives rise to an unprecedented diversity of derivatives. This unique feature leads to a vast number of products that may arise from addition of just one reagent. Substitution reactions can take place on derivatives, once these have been formed by addition. Some fullerenic compounds are briefly described below.

Group 14 Elements (a)

(b)

513

(c)

Fig. 14.2.5.

Fullerenes bonded to non-metallic elements: (a) C60 O, (b) C60 Br6 , and (c) C60 [OsO4 (pyBu)2 ].

(1) Fullerenes bonded to non-metallic elements This class of compounds consists of fullerene adducts with covalent bonds formed between the fullerene carbon atoms and non-metallic elements. Since all carbon atoms lie on the globular fullerene surface, the number of sites, as well as their positions, where additions take place vary from case to case. Examples of these compounds include C60 O, C60 (CH2 ), C60 (CMe3 ), C60 Br6 , C60 Br8 , C60 Br24 , C50 Cl10 , and C60 [OsO4 (pyBu)2 ]. In the first two examples, the oxygen atom and the methylene carbon atom are each bonded to two carbon atoms on a (6/6) edge in the fullerene skeleton. The structure of C60 O is shown in Fig. 14.2.5(a). In the next five examples, the C atom of CMe3 , as well as Br and Cl, is each bonded to only one carbon atom of fullerene. The structure of C60 Br6 is displayed in Fig. 14.2.5(b). In the final example, the six-coordinate osmium(VI) moiety OsO4 (pyBu)2 is linked to C60 through the formation of a pair of O–C single bonds with two neighboring carbon atoms in the fullerene skeleton, as shown in Fig. 14.2.5(c). (2) Coordination compounds of fullerene This class of coordination compounds features direct covalent bonds between complexed metal groups and the carbon atoms of fullerene systems. Monoadducts such as C60 Pt(PPh3 )2 each have only one group bonded to a fullerene, as shown in Fig. 14.2.6(a). Multiple adducts are formed when several groups are attached to the same fullerene nucleus. Typical examples are C60 [Pt(PPh3 )2 ]6 and C70 [Pt(PPh3 )2 ]4 , whose structures are displayed in Figs. 14.2.6(b) and 14.2.6(c), respectively. (3) Fullerenes as π-ligands In this class of metal complexes, there is delocalized π bonding between fullerene and the metal atom. The structures of (η5 -C5 H5 )Fe(η5 -C60 Me5 ) and (η5 -C5 H5 )Fe(η5 -C70 Me3 ), each containing a fused ferrocene moiety, are shown in Fig. 14.2.7. The shared pentagonal carbon ring of the C60 (or C70 ) skeleton acts as a 6π -electron donor ligand to the Fe(II) atom of the Fe(C5 H5 ) fragment. In (η5 -C5 H5 )Fe(η5 -C60 Me5 ), the five methyl groups attached to five sp3 carbon atoms protrude outward at an angle of 42◦ relative to the symmetry axis of the molecule. The C5 H5 group and cyclopentadienide in Fe(C60 Me5 ) are arranged in a staggered manner; the C–C bond lengths are 141.1 pm (averaged

514

Structural Chemistry of Selected Elements for C5 H5 ) and 142.5 pm (averaged for C60 Me5 ). The Fe–C distances are 203.3 pm for C5 H5 and 208.9 pm for C60 Me5 , which are comparable to those in known ferrocene derivatives. The structural features of (η5 -C5 H5 )Fe(η5 C70 Me3 ) are similar to those of (η5 -C5 H5 )Fe(η5 -C60 Me5 ). The C–C bond lengths in the shared pentagon are 141–3 pm. The Fe–C bond distances are 205.4 pm (averaged for C5 H5 ) and 208.3 pm (averaged for C70 Me3 ). (a)

45 109.2º 2.1 41.3º 102.4º 107.1º 2.115 2.303

2.253

(b)

(c)

Fig. 14.2.6.

Molecular structure of (a) C60 Pt(PPh3 )2 , (b) C60 [Pt(PPh3 )2 ]6 , and (c) C70 [Pt(PPh3 )2 ]4 .

(4) Metal fullerides Fullerenes exhibit an electron-accepting nature and react with strong reducing agents, such as the alkali metals, to yield metal fulleride salts. The compounds Li12 C60 , Na11 C60 , M6 C60 (M = K, Rb, Cs), K4 C60 and M3 C60 (M3 = K3 , Rb3 , RbCs2 ) have been prepared.

(a)

Fig. 14.2.7.

Structure of (a) (η5 -C5 H5 )Fe(η5 -C60 Me5 ) and (b) (η5 -C5 H5 )Fe(η5 -C70 Me3 ).

(b)

Group 14 Elements

515

The M3 C60 compounds are particularly interesting as they become superconducting materials at low temperature, with transition temperatures (Tc ) of 19 K for K3 C60 , 28 K for Rb3 C60 , and 33 K for RbCs2 C60 . Fulleride K3 C60 is a face-centered cubic crystal, space group Fm3m, with a = 1424(1) pm and Z = 4. The C60 3− ions form a ccp structure with K+ ions filling all the tetrahedral interstices (radius 112 pm) and octahedral interstices (radius 206 pm), as shown in Fig. 14.2.8. Both K4 C60 and Rb4 C60 are tetragonal, and the structure of M6 C60 at room temperature is body-centered cubic. These metal fullerides are all insulators. Fig. 14.2.8.

(5) Fullerenic supramolecular adducts Fullerenes C60 and C70 form supramolecular adducts with a variety of molecules, such as crown ethers, ferrocene, calixarene, and hydroquinone. In the solid state, the intermolecular interactions may involve ionic interaction, hydrogen bonding, and van der Waals forces. Figure 14.2.9 shows a part of the structure of [K(18C6)]3 ·C60 ·(C6 H5 CH3 )3 , in which C3− 60 is surrounded by a pair of [K+ (18C6)] complexed cations.

Crystal structure of K3 C60 (large circles represent C60 and small circles represent K).

K

(6) Fullerene oligomers and polymers This class of compounds contain two or more fullerenes and they may be further divided into the following three categories. (a) Dimers and polymers containing two or more fullerenes are linked together through C–C covalent bonds formed by the carbon atoms on the globular surface. Figure 14.2.10(a) shows the structure of dimeric [C60 (t Bu)]2 . In addition, chain-like polymeric fullerenes with the following structure have been proposed, although none has yet been prepared:

314 pm K

—[ C60 H2 —C60 H2 —C60 H2 ]— n (b) Two or more fullerenes are linked together through the formation of C–C covalent bonds with an organic functional group. Figure 14.2.10(b) shows the structure of [C60 ]3 (C14 H14 ), in which three fullerenes form an adduct through C-C linkage with the central C14 H14 unit. (a)

Fig. 14.2.9.

A part of the structure of [K(18C6)]3 ·C60 ·(C6 H5 CH3 )3 .

(b)

Fig. 14.2.10.

Structures of (a) [C60 (t Bu)]2 and (b) [C60 ]3 (C14 H14 ).

516

Structural Chemistry of Selected Elements (c) Fullerenes are linked as pendants at regular intervals to a skeleton of a polymeric chain, such as: CH–CR=CH–CH2

CH–CR=CH–CH2

C60H

C60H

(7) Heterofullerenes Heterofullerenes are fullerenes in which one or more carbon atoms in the cage are replaced by other main-group atoms. Compounds containing boron, such as C59 B, C58 B2 , C69 B, and C68 B2 , have been detected in the mass spectra of the products obtained using boron/graphite rods in arc discharge synthesis. Since nitrogen has one more electron than carbon, the azafullerenes are radicals (C59 N·, C69 N·), which can either dimerise to give (C59 N)2 and (C69 N)2 , or take up hydrogen to give C59 NH. (8) Endohedral fullerenes (incar-fullerenes) Fullerenes can encapsulate various atoms within the cages, and these compounds have been referred to as endohedral fullerenes. For example, the symbolic representations La@C60 and La2 @C80 indicate that the fullerene cage encapsulates one and two lanthanum atom(s), respectively. The IUPAC description refers to these fullerenes species as incar-fullerenes, and the formulas are written as iLaC60 and iLa2 C80 , (i is derived from incarcerane). Some metal endohedral fullerenes are listed in Table 14.2.1. The endohedral fullerenes are expected to have interesting and potentially very useful bulk properties as well as a fascinating chemistry. Some non-metallic elements, such as N, P, and noble gases, can be incarcerated into fullerenes to form N@C60 , P@C60 , N@C70 , Sc3 N@C80 , Ar@C60 , etc. Table 14.2.1. Endohedral fullerenes

Fullerene

Metallic atom

Fullerene

Metallic atom

C36 C44 C48 C50 C60

U K, La, U Cs U, La Li, Na, K, Rb, Cs, Ca, Ba, Co, Y, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Lu, U Li, Ca, Y, Ba, La, Ce, Gd, Lu, U U Ca, Sc, La, Gd, Lu La Ca, Sr, Ba La Ca, Sr, Ba, Sc, Y, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu Ca, Sr, Ba, Sc, La

C56 C60 C66 C74 C76 C79 N C80 C82

U2 Y2 , La2 , U2 Sc2 Sc2 La2 La2 La2 , Ce2 , Pr2 Er2 , Sc2 , Y2 , La2 , Lu2 , Sc2 C2 Sc2 , La2 , Sc2 C2 Sc3 N Sc3 N Sc3 N, ErSc2 N, Sc2 LaN, ScLa2 N, La3 N Sc3 Sc3 Sc4

C70 C72 C74 C76 C80 C81 N C82 C84

C84 C68 C78 C80 C82 C84 C82

Group 14 Elements (a)

(b)

(c)

(d)

517

Fig. 14.2.11.

Structures of some endofullerenes: (a) N@C60 , (b) Ca@C60 , (c) Sc3 N@C78 and (d) Sc2 C2 @C84 .

Theoretical and experimental studies of the structures and electronic properties of endohedral fullerenes have yielded many interesting results. The enclosed N and P atoms of N@C60 and P@C60 retain their atomic ground state configuration and are localized at the center of the fullerenes, as shown in Fig. 14.2.11(a). The atoms are almost freely suspended inside the respective molecular cages and exhibit properties resembling those of ions in electromagnetic traps. In Ca@C60 , the Ca atom lies at an off-center position by 70 pm, as shown in Fig. 14.2.11(b). The symmetry of Ca@C60 is predicted to be C5v , implying that the Ca atom lies on a fivefold rotation axis of the C60 cage. The predicted distances between the Ca atom and the first and second set of nearest C atoms are 279 and 293 pm, respectively. A single-crystal X-ray diffraction study of [Sc3 N@C78 ]·[Co(OEP)] ·1.5(C6 H6 )·0.3(CHCl3 ) (OEP is the dianion of octaethylporphyrin) showed that the fullerene is embraced by the eight ethyl groups of the porphyrin macrocycle. The structure of [Sc3 N@C78 ] is shown in Fig. 14.2.11(c). The N–Sc distances range from 198 to 212 pm, and the shortest C–Sc distances fall within a narrow range of 202–11 pm. The flat Sc3 N unit is oriented so that it lies near the equatorial mirror plane of the C78 cage. A synchrotron X-ray powder diffraction study of (Sc2 C2 )@C84 showed that the lozenge-shaped Sc2 C2 unit is encapsulated by the D2d -C84 fullerene, as shown in Fig. 14.2.11(d). The Sc–Sc, Sc–C and C–C distances in the Sc2 C2 unit are 429, 226 and 142 pm, respectively.

14.3

Bonding in carbon compounds

14.3.1

Types of bonds formed by the carbon atom

The capacity of the carbon atom to form various types of covalent bonds is attributable to its unique characteristics as an element in the Periodic Table.

518

Structural Chemistry of Selected Elements Table 14.3.1. Hybridization schemes of carbon atom

Number of orbitals Interorbital angle Geometry % s character % p character Electronegativity of carbon Remaining p orbitals

sp

sp2

sp3

2 180◦ Linear 50 50 3.29 2

3 120◦ Trigonal 33 67 2.75 1

4 109.47◦ Tetrahedral 25 75 2.48 0

The electronegativity of the carbon atom is 2.5, which means that the carbon atom cannot easily gain or lose electrons to form an anion or cation. As the number of valence orbitals is exactly equal to the number of valence electrons, the carbon atom cannot easily form a lone pair or electron-deficient bonds. Carbon has a small atomic radius, so its orbitals can overlap effectively with the orbitals of neighbor atoms in a molecule. For simplicity, we use the conventional concept of hybridization to describe the bond types, but bonding is frequently more subtle and more extended than implied by this localized description. The parameters of typical hybridization schemes of the carbon atom are listed in Table 14.3.1. The hybrid orbitals of carbon always overlap with orbitals of other atoms in a molecule to form σ bonds. The remaining p orbitals can then be used to form π bonds, which can be classified into two categories: localized and delocalized. The localized π bonds of carbon form double and triple bonds as illustrated below:

The carbon atom can also form σ and π bonds to metal atoms in various fashions. For example: (a)

C

(b)

M

single bond

C M

C M

,

M

M

, polycenter metal-carbon bonds

M

(c)

C

M

double bond

(d)

C

M

triple bond

Group 14 Elements

519

A particularly interesting example is the tungsten complex R Me2 C P W P Me2

CHR

,

R = CMe3

CH2R

which contains C≡W, C=W, and C–W bonds with lengths 179, 194, and 226 pm, respectively. The delocalized π bonds involve three or more carbon atoms or heteroatoms. For instance:

An enormous variety of π-bonded systems, whether they be neutral or ionic, cyclic or linear, odd or even in the number of carbon atoms, serve as ligands that coordinate to transition metals. Figure 14.3.1 shows some representatives of the innumerable organometallic coordination compounds stabilized by metal-π bonding. Larger aromatic rings and polycyclic aromatic hydrocarbons can also function as π ligands in forming sandwich-type metal complexes. For example, the planar cyclooctatetraenyl dianion C8 H8 2− functions as a η8 -ligand to form the sandwich compound uranocene, U(C8 H8 )2 , which takes the eclipsed configuration. Recently the “sandwich” motif has been extended to the case of two cyclic aromatic ligands flanking a small planar aggregate of metal atoms. In [Pd3 (η7 C7 H7 )2 Cl3 ](PPh4 ), a triangular unit of palladium(0) atoms each coordinated by

Fig. 14.3.1.

Some examples of organometallic compounds formed with π bonding ligands.

520

Structural Chemistry of Selected Elements (a)

(b)

(c)

2+

+ Pd Cl

Pd

Cl Pd

+

Pd Cl

Pd

Pd Pd

Pd

Fig. 14.3.2.

(a) Molecular geometry and (b) structural formula of the [Pd3 (η7 -C7 H7 )2 Cl3 ]− ion; the Pd–C and Pd· · ·C bond lengths are in the ranges 215–47 and 253–61 pm, respectively. (c) Structure of the [Pd5 (C18 H12 )2 (C7 H8 )]2+ ion; coordination of an electronically delocalized C3 fragment to a Pd center is represented by a broken line.

a terminal chloride ligand is sandwiched between two planar cycloheptatrienyl C7 H7 + rings, as shown in Figs. 14.3.2(a, b). The measured Pd–Pd (274.5 to 278.9 pm) and Pd–Cl (244.2 to 247.1 pm) bonds are within the normal ranges. In [Pd5 (naphthacene)2 (toluene)][B(Arf )4 ]2 ·3toluene, where Arf = 3,5(CF3 )2 C6 H3 , the sheet-like pentapalladium(0) core is composed of a triangle sharing an edge with a trapezoid; the innermost Pd–Pd distance (291.6 pm) is relatively long. This metal monolayer is sandwiched between two naphthacene radical cations, each of which coordinates to the Pd5 sheet through 12 carbons via the µ5 –η2 :η2 :η2 :η3 :η3 mode, as illustrated in Fig. 14.3.2(c). One of the four independent toluene molecules in the unit cell is located near the apex Pd atom at a closest contact of 252 pm, but its coordination mode (either η2 or η1 ) cannot be definitively assigned owing to disorder. 14.3.2

Coordination numbers of carbon

Carbon is known with all coordination numbers from 0 to 8. Some typical examples are given in Table 14.3.2, and their structures are shown in Fig. 14.3.3. In these examples, the compounds with the high coordination numbers, such as ≥ 5, do not belong to the class of hypervalent compounds, but rather to electron-deficient systems. Hypervalent molecules usually have a central atom which requires the presence of more than an octet of electrons to form more than four 2c-2e bonds, such as the S atom in SF6 . 14.3.3

Bond lengths of C–C and C–X bonds

The bond lengths of carbon–carbon bonds are listed in Table 14.3.3. The bond lengths of some important bond types of carbon–heteroatom bonds are given in Table 14.3.4. The values given here are average values from experimental determinations and do not necessarily exactly apply to a particular compound. 14.3.4

Factors influencing bond lengths

The measured bond lengths in a molecule provide valuable information on its structure and properties. Some factors that influence the bond lengths are discussed below.

Group 14 Elements

521

Table 14.3.2. Coordination numbers of carbon

Coordination number

Examples

Structure in Fig. 14.3.2

0 1 2 2 2 3 3 3 4 4 5 5 6 6 7 8

C atoms, gas phase CO, stable gas CO2 , stable gas HCN, stable gas :CX2 (carbene), X = H, F, OH C=OXY (oxohalides, ketones) CH3 − , CPh3 − Ta(=CHCMe3 )2 (Me3 C6 H2 )(PMe3 )2 CX4 (X = H, F, Cl) Fe4 C(CO)13 Al2 Me6 (Ph3 PAu)5 C+ · BF4 − [Ph3 PAu]6 C2+ C2 B10 H12 [LiMe]4 crystal [(Co8 C(CO)18 ]2−

(a) (b) Linear (c) Linear (d) Bent (e) Planar (f) Pyramidal (g) T-shaped∗ (h) Tetrahedral (i) C capping Fe4 (j) Bridged dimer (k) Trigonal bipyramidal (l) Octahedral (m) Pentagonal pyramidal (n) † (o) Cubic

∗ The

unique H is equatorial and angle Ta=C–CMe3 is 169◦ . distance of intramolecular C–Li is 231 pm, (a C atom caps 3 Li atoms in each face of the Li4 tetrahedron), C–H is 96 pm, and intermolecular C–Li is 236 pm. † The

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m)

(n)

(o)

Fig. 14.3.3.

Coordination numbers of carbon in its compounds.

(1) Bonds between atoms of different electronegativities It is generally found that the greater the difference in electronegativity between the bonding atoms, the greater the deviation from the predicted bond distance based on covalent radii or the mean values given in Tables 14.3.3 and 14.3.4. Empirical methods for the adjustment of covalent bond lengths by a factor dependent on the electronegativity differences between the atoms have been proposed.

522

Structural Chemistry of Selected Elements Table 14.3.3. Bond lengths (in pm) of carbon–carbon bonds

Bond

Bond length

Example

C–C sp3 –sp3 sp3 –sp2 sp3 –sp sp2 –sp2 sp2 –sp sp–sp

153 151 147 148 143 138

Ethane (H3 C–CH3 ) Propene (H3 C–CH=CH2 ) Propyne (H3 C–C≡CH) Butadiene (H2 C=CH–CH=CH2 ) Vinylacetylene (H2 C=CH–C≡CH) Butadiyne (HC≡C–C≡CH)

C=C sp2 –sp2 sp2 –sp sp–sp

132 131 128

Ethylene (H2 C=CH2 ) Allene (H2 C=C=CH2 ) Butatriene (H2 C=C=C=CH2 )

C≡C sp–sp

118

Acetylene (HC≡CH)

Table 14.3.4. Bond lengths (in pm) of C–X bonds

C–N C–H

sp3 –H sp2 –H sp–H

C–O

C=O

sp3 –O sp2 –O sp3 –O sp2 –O

109 108 108

C=N

C–S

sp3 –N sp2 –N

147 138

sp2 –N

128

C=S

sp–N

114

C–Si

sp3 –P

185

C=Si

sp2 –P

166

sp–P Cl 179 173 163

154

C≡N 143 134 121 116

C–P C=P

sp3 –S sp2 –S sp–S

182 175 168

sp2 –S

167

sp3 –Si

189

sp2 –Si

170

C≡P C–X

X= sp3 –X sp2 –X sp–X

F 140 134 127

Br 197 188 179

I 216 210 199

(2) Steric strain Steric strain exists in a molecule when bonds are forced to make abnormal angles. There are in general two kinds of structural features that result in sterically-caused abnormal bond angles. One of these is common to small ring compounds, where the bond angles must be less than those resulting from normal orbital overlap. Such strain is called small-angle strain. The other arises when nonbonded atoms are forced into close proximity by the geometry of the molecule. This effect is known as steric overcrowding. Steric strain generally leads to elongated bond lengths as compared to the expected values given in Tables 14.3.3 and 14.3.4.

Group 14 Elements

523

(3) Conjugation A hybrid atomic orbital of higher s content has a smaller size and lies closer to the nucleus. Accordingly, carbon–carbon bonds are shortened by increasing s character of the overlapping hybrid orbitals. The C(sp3 )–C(sp3 ) single bond is generally longer than other single bonds involving sp2 and sp carbon atoms. This general rule arises mainly from conjugation between the bonded atoms. When mean values are used to estimate bond lengths, the conjugation factor must be taken into account. For example, the C–C bond length in benzene is 139.8 pm, which is virtually equal to the mean value of the C(sp2 )–C(sp2 ) and C=C bond lengths: 12 (148 + 132) = 140 pm. Hence the conjugation of alternating single and double bonds in benzene can be expressed as resonance between two limiting valence bond (canonical) structures:

(4) Hyperconjugation The overlap of a C–H σ orbital with the π (or p) orbital on a directly bonded carbon atom is termed hyperconjugation. This interaction has a shortening effect on the C–C bond length, a good example being the structure of the tert-butyl cation [C(CH3 )3 ]+ . (a)

(b)

Fig. 14.3.4.

Hyperconjugation in [C(CH3 )3 ]+ : (a) structure of [C(CH3 )3 ]+ and (b) hyperconjugation between central carbon atom C(1) and one of the C–H σ bonds.

The structure of [C(CH3 )3 ]+ in the crystalline salt [C(CH3 )3 ]Sb2 F11 is shown in Fig. 14.3.4(a). The carbon skeleton is planar with an average C–C bond length of 144.2 pm and approximate D3h molecular symmetry. The experimental C–C bond length is shorter by 6.8 pm than the normal C(sp3 )-C(sp2 ) bond length of 151 pm. This is due to hyperconjugative interaction between three filled C–H σ bond orbitals and the empty p orbital on the central carbon atom that leads to partial C–C π bonding, as shown in Fig. 14.3.4 (b). (5) Surroundings of bonding atoms The geometry and connected groups of bonding atoms usually influence the bond lengths. For example, an analysis of C–OR bond distances in more than 2000 ethers and carboxylic esters (all with sp3 carbon) showed that this distance increases with increasing electron-withdrawing power of the R group, and also when the C atom changes from primary through secondary to tertiary. For such compounds mean C–O bond lengths range from 141.8 to 147.5 pm.

524

Structural Chemistry of Selected Elements As an illustrative example taken from the current literature, consider the variation of C–C and C–O bond lengths in the deltate species C3 O2− 3 held within a dinuclear organometallic uranium(IV) complex. In a remarkable synthesis, this cyclic aromatic oxocarbon dianion is generated by the metal-mediated reductive cyclotrimerization of carbon monoxide, as indicated in the reaction scheme R R UCl3

(i) KCp*, THF

R

(ii) K2[COT(1,4-SiiPr3)], THF

O

–78

O

R

CO, pentane U

U

25 C

O

U O i

R

R = Si Pr3

R

A strongly reducing organouranium(III) complex stabilized by η5 cyclopentadienide and η8 -cyclooctatetraenediide ligands, together with tetrahydrofuran, is used to crack the robust C≡O triple bond at room temperature and ambient pressure. Low-temperature X-ray analysis revealed the presence of a reductively homologated CO trimer, C3 O3 2− , as a η1 :η2 bridging ligand between two organouranium(IV) centers. The measured dimensions of the central molecular skeleton are shown below: 127.7(5) 218.3(3) pm

137.7(6) 130.3(5)

α

138.1(6)

248.4(3) 265.4(4)

β γ

α = 58.5º β = 58.7º γ = 62.8º

143.6(7) 267.0(4)

126.2(5)

251.6(3)

The noticeable distortion of the C3 ring and measured C–C, C–O and U– O bond lengths reflect the conjugation effect, the chemical environment of individual atoms, steric congestion around the respective uranium centers, and variation caused by experimental errors. 14.3.5

Abnormal carbon–carbon single bonds

(1) Unusually long C–C bonds Figure 14.3.5 shows some organic molecules which have abnormally long C–C bonds. Rationalization of these unusual structures is discussed below. (a)

Oxalic acid, HOOC–COOH

−C==O system which satisfies the In the oxalic acid molecule, there is a O==C− condition for conjugation, and the existence of delocalized π bonding has been

Group 14 Elements (a)

(b)

(d)

525

(c)

(e) Fig. 14.3.5.

Some molecules with abnormally long C–C bonds (lengths in pm): (a) oxalic acid, (b) cubane, (c) skeleton of Dewar benzene derivative, (d) 1-cyano-tetracyclodecane, and (e) paracyclophane.

substantiated by deformation density studies. The central C(sp2 )–C(sp2 ) bond has a length of 156.8 pm. A MNDO computation showed that the four fully occupied π MOs are alternately bonding and antibonding orbitals between the two C atoms. Thus the π MOs contribute little to bonding. The σ bond order is less than unity mainly because each carbon atom is bonded to two highly electronegative oxygen atoms, leading to a reduction of charge density on the carbon atom. The bond order in the C–C bond is made up of a σ component of 0.815 and a π component of only 0.015. The strongly reducing properties of oxalic acid are associated with its relatively weak C–C bond which easily cleaves during a reaction, and the resulting fragments are then oxidized to carbon dioxide. (b) Cubane, C8 H8 Several cubane structures have been determined. The mean C–C bond length is 155.6 pm from 42 independent measurements of the edges. This long bond length can be understood by considering the lesser overlap of endocyclic orbitals that are richer in p character than the typical sp3 hybrid. (c) Dewar benzene derivatives In derivatives of Dewar benzene, the bond length of the bridging C–C bond is found to lie in the range 156–159 pm. The elongation of bond length is mainly due to the strain caused by the fusion of two four-membered rings. (d) 1-Cyano-tetracyclodecane, C10 H13 CN In this molecule, the pair of bridgehead atoms each has all four bonds directed to the same side as its partner atom, and the central bond length is 164.3 pm. Thus the bridgehead atoms have an “inverted” bond configuration and serious C–C bond strain. (e) [2.2]Paracyclophane, C16 H16 In the cyclophanes, the bridging bond lengths are generally the longest and in some instances have been found to be near or greater than 160 pm. The

526

Structural Chemistry of Selected Elements (a)

(b) CAr3

167(3)

(c)

Ph Ph Ph Ph

164.8(3)

t-Bu

X

Ar =

173.3(6) (X = I) 171.0(2) (X = Cl)

t-Bu

(d)

X

CAr3

t-Bu

t-Bu Ph

Ph

Ph

Ph

t-Bu Ph

Ph

Ph

140.1(5) 140.1(5)

147.1(5)

154.0(5)

t-Bu

Ia

Ph

Ph t-Bu

Ib

(e)

Ph

Ph

141.3(5) 141.7(5)

Ph

t-Bu 132.9(3) 142.0(4)

140.7(2) 138.1(2) 149.4(3)

149.0(3)

134.8(2)

Fig. 14.3.6.

Molecules containing very long C–C single bonds. The bond lengths are shown in pm.

IIa

IIb

elongation of the C–C single bond in the bridging –CH2 –CH2 – group of [2.2]paracyclophane is attributable to the inherent steric strain. Further examples of organic molecules containing very long carbon–carbon single bonds have been reported in recent years. The extended C(sp3 )–C(sp3 ) bond in the hexaarylethane shown in Fig. 14.3.6(a) is caused by severe steric repulsion between the bulky substituted phenyl groups. In the bi(anthracene9,10-dimethylene) photodimer shown in Fig. 14.3.6(b), the bridge bond of the cyclobutane ring has a length longer than the rest. Extremely long C(sp3 )– C(sp3 ) bonds have been shown to exist in the naphthocyclobutenes shown in Fig. 14.3.6(c). The bond length variation in the substituted benzodicyclobutadiene shown in Fig. 14.3.6(d), as determined from X-ray analysis, can be fairly well accounted for by resonance between the canonical formulas Ia and Ib. The central sixmembered ring contains a pair of extremely long C(sp2 )–C(sp2 ) bonds at 154.0(5) pm, which significantly exceed the reference bond distance of 149.0(3) pm observed for tris(benzocyclobutadieno)benzene [Fig. 14.3.6(e)]. The bond length pattern in the latter compound indicates that its structure is better described by the radiallene formula IIa in preference to formula IIb, which contains anti-aromatic cyclobutadiene moieties. (2) Unusually short bonds between tetracoordinate carbon atoms Figure 14.3.7 shows some organic molecules containing abnormally short single bonds between two four-coordinate carbon atoms.

Group 14 Elements (a)

(b)

(c)

140.8(2) (R = Me) 144.4(3) (R = Ph) R

145.8(8)

H3COOC

R

527

(CH2)n (CH2)n 144.0 (n = 2) 144.5 (n = 3)

COOCH3

O

H

(e)

(d) SiMe3

d = 147.5(6); 149.5(6)

SiMe3

Me

143.6(3)

SiMe3

O2S SiMe3

SiMe3

SO2 SO2

SiMe3

The bond between two bridgehead carbon atoms in bicyclo[1.1.0]butane exhibits the properties of a carbon–carbon multiple bond, although it is formally a single bond. The dihedral angle δ between the three-membered rings in 1,5-dimethyltricyclo[2.1.0.0]pentan-3-one is made small by the short span of the carbonyl linkage, as shown in Fig. 14.3.7(a). The bridgehead bond has a pronounced π character with a length of 140.8(2) pm. In the 1,5-diphenyl analog, the two aromatic rings are oriented almost perpendicular (at 93.6◦ and 93.6◦ ) to the plane bisecting the angle δ. There is optimal conjugation between the phenyl groups via the π-population of the bridge bond, and the conjugation effect leads to its lengthening of the latter to 144.4(3) pm. The central exocyclic C(sp3 )–C(sp3 ) bond connecting two bicyclobutane moieties is quite short [Fig. 14.3.7(b)], as are the related linkages in bicubyl [Fig. 14.3.7(c)] and hexakis(trimethylsilyl)bitetrahedryl [Fig. 14.3.7(d)]. The calculated s character of the linking C–C bond in the bitetrahedryl molecule is sp1.53 , which is consistent with its significant shortening. In the crystal structure of the in-isomer of the methylcyclophane shown in Fig. 14.3.7(e), there are two independent molecules with measured C–Me bond distances of 147.5(6) and 149.5(6) pm. The inward-pointing methyl group is forced into close contact with the basal aromatic ring, and the steric congestion accounts for compression of the C–Me bond. 14.3.6

Complexes containing a naked carbon atom

In the realm of all-carbon ligands in the formation of transition-metal complexes, the naked carbon atom holds a special position. Based on the geometry of metal–carbon interaction, these compounds can be divided into four classes: terminal carbide (I), 1,3-dimetallaallene (II), C-metalated carbyne (III), and carbido cluster (IV): :C

M (I)

M

C (II)

M

M

C (III)

M

C@Mn (IV)

Fig. 14.3.7.

Molecules containing very short C–C single bonds. The bond lengths are shown in pm. Values are given for two independent molecules of compound (e).

528

Structural Chemistry of Selected Elements .. _ C Mo

Fig. 14.3.8.

Complexes containing a metal–terminal carbon triple bond.

Ar(R)N

L Cl Ru N(R)Ar

C:

_

Cl

N(R)Ar

L

There are two well-characterized examples of a naked carbon atom bound by a triple bond to a metal center (Fig 14.3.8). The molybdenum carbide 5− 4 (R = C(CD3 )2 (CH3 ), Ar = C6 H3 Me2 -3,5), an anion CMo{N(R)Ar}3 isoelectronic analog of NMo{N(R)Ar}3 , can be prepared in a multistep procedure via deprotonation of the d0 methylidyne complex HCMo{N(R)Ar}3 . The Mo≡C distance of 171.3(9) pm is at the low end of the known range for molybdenum–carbon multiple bonds. In the diamagnetic, air-stable terminal ruthenium carbide complex Ru(≡C:)Cl2 (LL, )(L = L, = PCy3 , or L = PCy3 and L, = 1,3-dimesityl-4,5-dihydroimidazol-2-ylidene), the measured Ru–C distance of 165.0(2) pm is consistent with the existence of a very short Ru≡C triple bond. Many complexes containing a M–C–M, bridge have been reported. The earliest know example of a 1,3-dimetallallene complex, {Fe(tpp)}2 C (tpp = tetraphenylporphyrin), was synthesized by the reaction of Fe(tpp) with CI4 , CCl3 SiMe3 , CH2 Cl2 and BuLi. The single carbon atom bridges the two Fe(tpp) moieties with Fe–C 167.5(1) pm in the linear Fe–C–Fe unit. Thermal decomposition of the olefin metathesis catalyst (IMesH2 )(PCy3 )(Cl)2 Ru=CH2 (IMesH2 = 1,3-dimesityl-4,5-dihydroimidazol-2-ylidene) results in the formation of a C-bridged dinuclear ruthenium complex, as shown in the following scheme. The Ru≡C–Ru bond angle is 160.3(2)◦ . The measured Ru≡C bond distance of 169.8(4) pm is slightly longer than those in reported µ-carbide ruthenium complexes such as (PCy3 )2 (Cl)2 Ru≡C–Pd(Cl)2 (SMe2 ) (166.2(2) pm), and the Ru–C distance of 187.5(4) pm is much shorter than the usual R–C single bonds in ruthenium complexes such as (Me3 CO)3 W≡C–Ru(CO)2 (Cp) (209(2) pm).

N

Cl Cy3P

N

Ru CH2 Cl

55 oC 0.023 M C6H6

N Mes N N

+ CH3PCy3 + Cl–

N

Ru C

Ru

H

Cl

Cl Cl

Mes

The carbide-centered polynuclear transition-metal carbonyl clusters exhibit a rich variety of structures. A common feature to this class of carbide complexes is that the naked carbon is wholly or partially enclosed in a metal cage composed of homo/hetero metal atoms, and there is also a subclass that can be considered as tetra-metal-substituted methanes. The earliest known compound of this kind is Fe5 C(CO)15 , in which the carbon atom is located at the center

Group 14 Elements (a)

(b)

Ru(CO)3

(OC)3Ru

C

529

Ru(CO)3

C

(OC)2Ru

Ru(CO)2 C

Ru(CO)3

(c)

O

(d)

Fe(CO)3

C=O

Fe (CO)3

Fe(CO)3 C

Fe(CO)3

(OC)3Fe

n-

RC

(OC)3Fe

C

(OC)3Fe

= Os(CO)3

(OC)3Co

= Os(CO)2

(e) Me Me

Me Al

Me Al

N

Co(CO)3 t-Bu3P

Co (CO)3

Me

Me

C

Ti

Ti

C

t-Bu3P N Al Me Me

Al Me Me

of the base of a square pyramid with Fe(CO)3 groups occupying its five vertices. Carbido carbonyl clusters of Ru and Os are well documented. Octahedral Ru6 C(CO)17 is composed of four Ru(CO)3 and two cis-Ru(CO)2 fragments, the latter being bridged by a carbonyl group [Fig. 14.3.9(a)]. Os10 C(CO)24 is built of an octahedral arrangement of Os(CO)2 groups with four of its eight faces each capped by an Os(CO)3 group, as shown in Fig. 14.3.9(b). The exposed carbon atom in Fe4 C(CO)13 shows the greatest chemical activity, and the Fe4 C system serves as a plausible model for a surface carbon atom in heterogeneous catalytic processes [Fig. 14.3.9(c)]. Addition of Co3 (µ3 -CCl)(CO)9 to a solution of (PPh4 )2 [Fe3 (µ-CCO)(CO)9 ] (CCO is the ketenylidene group C=C=O) in CH2 Cl2 , in the presence of thallium salt, generates the species [{Co3 (CO)9 }C{Fe3 (CO)9 (µ-CCO)}]− containing a single carbon atom linking two different trimetallic clusters; subsequent addition of ethanol yielded the complex [{Co3 (CO)9 }C{Fe3 (CO)9 (µ-C–CO2 Et)}]2− . The structures of these two hexanuclear hetereometallic anions are shown in Fig. 14.3.9(d). The reaction of AlMe3 with (t-Bu3 PN)2 TiMe2 leads to the formation of two Ti complexes, of which [(µ2 -t-Bu3 PN)Ti(µ-Me)(µ4 -C)(AlMe2 )2 ]2 is the major product. Single-crystal X-ray analysis revealed that it has a saddle-like structure, with two phosphinimide ligands lying on one side and four AlMe2 groups on the other [Fig. 14.3.9(e)]. The Ti and carbide C atoms in the central Ti2 C2 ring both exhibit distorted tetrahedral coordination geometry.

14.3.7

Complexes containing naked dicarbon ligands

There is an interesting series of heterobinuclear complexes in which the Ru and Zr centers are connected by three different types of C2 bridges: C–C, C=C, and C≡C.

Fig. 14.3.9.

Molecular structures of some transition-metal clusters containing a naked carbon atom.

530

Structural Chemistry of Selected Elements Cp(Me3P)2RuC

CH

[Cp2Zr(Cl)(NMe2)] Cp(Me3P)2Ru

C

C

ZrCp2Cl

[Cp2Zr(Cl)(H)] Cp(Me3P)2Ru

H

H

[Cp2Zr(Cl)(H)]

C H

ZrCp2Cl

H2 C

Cp(Me3P)2Ru

ZrCp2Cl

H

In polynuclear metal complexes bearing a naked C2 species, multiple metal– carbon interactions generally occur, and the measured carbon–carbon bond distances indicate that the C2 ligand may be considered to originate from fully deprotonated ethane, ethylene, or acetylene, which is stabilized in a “permetallated” coordination environment. Singly and doubly bonded dicarbon moieties are found in some polynuclear transition-metal carbonyl complexes (carbon– carbon bond length in pm): Rh12 (C2 )(CO)25 , 148(2); [Co6 Ni2 (C2 )2 (CO)16 ]2− , 149(1); Fe2 Ru6 (µ6 -C2 )2 (µ-CO)3 (CO)14 Cp2 , 133.4(8) and 135.4(7); Ru6 (µ6 C2 )(µ-SMe2 )2 (µ-PPh2 )2 (CO)14 , 138.1(8). The following discussion is concerned only with anionic species derived from acetylene. Acetylene is a Brønsted acid (pKa ∼25). Its chemistry is associated with its triple-bond character and the labile hydrogen atoms. It can easily lose one proton to form the acetylide monoanion HC≡C− (IUPAC name acetylenide) or release two to give the acetylide dianion − C≡C− (C2 2− , IUPAC name acetylenediide). The acetylenide H–C≡C− and substituted derivatives R–C≡C− form organometallic compounds with the alkali metals. In these compounds, the interactions of the π orbitals of the C≡C fragment with metal orbitals may lead to many structural types, e.g., R–C ≡ C–Li Li–C ≡ C–R

The acetylenediide C2− 2 can combine with alkali and alkaline-earth metals to form ionic salts, which are readily decomposed by water. Four modifications of CaC2 (commonly known as calcium carbide) are known: room-temperature tetragonal CaC2 I, high-temperature cubic CaC2 IV (in which the C2− 2 dianion exhibits orientational disorder), low-temperature CaC2 II, and a fourth modification CaC2 III (Fig. 14.3.10). MgC2 , SrC2 , and BaC2 adopt the tetragonal CaC2 I structure, which consists of a packing of Ca2+ and discrete C2− 2 ions 2− in a distorted NaCl lattice, with the C2 dumbbell (bond length 119.1 pm from neutron powder diffraction) aligned parallel to the c axis. Ternary metal acetylenediides of composition AMI C2 (A = Li to Cs and I M = Ag(I), Au(I); or A = Na to Cs and MI = Cu(I)) have been prepared; NaAgC2 , KAgC2 , and RbAgC2 are isomorphous [Fig. 14.3.11(a)], but LiAgC2 [Fig. 14.3.11(b)] and CsAgC2 [Fig. 14.3.11(c)] belong to different structural types. The ternary acetylenediides A2 MC2 (A = Na to Cs, M = Pd, Pt) crystallize in the same structure type, which is characterized by [M(C2 )2/2 2− ]∞ chains

Group 14 Elements (a)

(b)

(c)

531

(d)

Fig. 14.3.10.

b

b a b

a

c

c

Crystal structure of (a) tetragonal CaC2 I (I 4/mmm, Z = 2); (b) cubic CaC2 IV ¯ Z = 4), the C2 2− dumbbell (Fm3m, exhibits orientational disorder; (c) low-temperature CaC2 II (C2/c, Z = 4); (d) meta-stable CaC2 III (C2/m, Z = 4).

c

a b

a

c

separated by alkali metal ions [Fig. 14.3.11(d)]. The ternary alkaline-earth acetylenediide Ba3 Ge4 C2 can be synthesized from the elements or by the reaction of BaC2 with BaGe2 at 1530 K; it consists of slightly compressed tetrahedral [Ge4 ]4− anions inserted into a twisted octahedral Ba6/2 three-dimensional framework. The Ba6 octahedra are centered by C2 2− dumbbells (C–C bond length 120(6) pm), which are statistically oriented in two directions. (a)

(b)

(c)

(d)

Fig. 14.3.11. c

b

b a

c

c

c

b

b a

a

a

The group 11 (Cu2 C2 , Ag2 C2 , and Au2 C2 ) and group 12 (ZnC2 , CdC2 and Hg2 C2 ·H2 O, and Hg2 C2 ) acetylenediides exhibit properties characteristic of covalent polymeric solids, but their tendency to detonate upon mechanical shock and insolubility in common solvents present serious difficulties in structural characterization. The earliest known and most studied non-ionic acetylenediide is Ag2 C2 (commonly known as silver acetylide or silver carbide), which forms a series of double salts of the general formula Ag2 C2 ·mAgX, − 2− 1 where X− = Cl− , I− , NO− 3 , H2AsO4 , or 2 EO4 (E = S, Se, Cr, or W), and m is the molar ratio. From 1998 onward, systematic studies have yielded a wide range of double, triple, and quadruple salts of silver(I) containing silver acetylenediide as a component, e.g., Ag2 C2 · mAgNO3 (m = 1, 5, 5.5, and 6), Ag2 C2 ·8AgF, Ag2 C2 ·2AgClO4 ·2H2 O, Ag2 C2 ·AgF·4AgCF3 SO3 ·RCN (R = CH3 , C2 H5 ) and 2Ag2 C2 ·3AgCN·15AgCF3 CO2 ·2AgBF4 ·9H2 O. A structural feature common to these compounds is that the C2 2− species is fully encapsulated inside a polyhedron with Ag(I) at each vertex, which may be represented as C2 @Agn . Note that each C2 @Agn cage carries a charge of (n−2)+, and such cages are linked by anionic (and co-existing neutral) ligands to form a two- or three-dimensional coordination network. Some polyhedral Agn cages with encapsulated C2 2− species found in various silver(I) double salts are shown in Fig. 14.3.12. In Ag2 C2 ·6AgNO3 , the dumbbell-like C2 2− moiety is located inside a rhombohedral silver cage whose edges lie

Crystal structure of (a) KAgC2 ¯ (P4/mmm, Z = 1); (b) LiAgC2 (P 6m2, Z = 1); (c) CsAgCz2 (P42 /mmc, Z = 2); ¯ Z = 1). (d) Na2 PdC2 (P 3m1,

532

Structural Chemistry of Selected Elements (a)

(b)

(c)

Fig. 14.3.12.

Polyhedral Agn (n = 6-9) cages with encapsulated C2 2− species found in various silver(I) double salts: (a) Ag2 C2 ·2AgClO4 ·2H2 O; (b) Ag2 C2 ·AgNO3 ; (c) Ag2 C2 ·5.5AgNO3 ·0.5H2 O; (d) Ag2 C2 ·5AgNO3 ; (e) Ag2 C2 ·6AgNO3 (the C2 2− group is shown in one of its three possible orientations); (f) Ag2 C2 ·8AgF. Other ligands bonded to the silver vertices are not shown. The dotted lines represent polyhedral edges that exceed 340 pm (twice the van der Waals radius of the Ag atom).

C2@Ag6

C2@Ag6

(d)

C2@Ag7

(e)

C2@Ag7

(f)

C2@Ag8

C2@Ag9

in the range of 295–305 pm, but it exhibits orientational disorder about a crystallographic threefold axis [Fig. 14.3.12(e)]. The utilization of C2 @Agn polyhedra as building blocks for the supramolecular assembly of new coordination frameworks has resulted in a series of discrete, 1-D, 2-D, and 3-D complexes bearing interesting structural motifs; further details are presented in Section 20.4.5. (a)

(b) Ph2P

PPh2

Fig. 14.3.13.

Structure of the tetranuclear molecular cation in (a) [Cu4 (µ-η1 : η2 -C≡C)(µdppm)4 ](BF4 )2 and (b) [Cu4 (µ-Ph2 Ppypz)4 (µη1 : η2 -C≡C)](ClO4 )2 ·3CH2 Cl2 .

Cu

Ph2P

C

Cu Ph2P

PPh2 Ph2P

PPh2

Cu C

Ph2P PPh2

Cu

PPh2

N

N Cu Cu N

N N

Cu Ph2P

C

C N N

N

N N Cu

N N

PPh2

To date, there are only two well-characterized copper(I) acetylenediide complexes. In [Cu4 (µ-η1 :η2 -C≡C)(µ-dppm)4 ](BF4 )2 (dppm = Ph2 PCH2 PPh2 ), the cation contains a saddle-like Cu4 (µ-dppm)4 system, with the C2 unit surrounded by a distorted rectangular Cu4 array and interacting with the Cu atoms in η1 and η2 modes [Fig. 14.3.13(a)]. In comparison, the tetranuclear, C2 symmetric cation of [Cu4 (µ-Ph2 Ppypz)4 (µ-η1 :η2 -C≡C)](ClO4 )2 ·3CH2 Cl2 [Ph2 Ppypz = 2-(diphenylphosphino-6-pyrazolyl)pyridine] consists of a butterfly-shaped Cu4 C2 core in which the acetylenediide anion bridges a pair of Cu2 subunits in both η1 and η2 bonding modes; the C≡C bond length is 126(1) pm [Fig. 14.3.13(b)].

Group 14 Elements 14.4

533

Structural chemistry of silicon

After oxygen (approx 45.5 wt%), silicon is the next most abundant element in the earth’s crust (approx 27 wt%). Elemental Si does not occur naturally, but it combines with oxygen to form a large number of silicate minerals. 14.4.1

Comparison of silicon and carbon

Silicon and carbon command dominant positions in inorganic chemistry (silicates) and organic chemistry (hydrocarbons and their derivatives), respectively. Although they have similar valence electronic configurations, [He]2s2 2p2 for C and [Ne]3s2 3p2 for Si, their properties are not similar. The reasons for the difference between the chemistry of the two elements are elaborated below. (1) Electronegativity The electronegativity of C is 2.54, as compared with 1.92 for Si. Carbon is strictly nonmetallic whereas Si is essentially a non-metallic element with some metalloid properties. (2) Configuration of valence shell and multiplicity of bonding Unlike carbon, the valence shell of the silicon atom has available d orbitals. In many silicon compounds, the d orbitals of Si contribute to the hybrid orbitals and Si forms more than four 2c-2e covalent bonds. For example, SiF5 − uses sp3 d hybrid orbitals to form five Si–F bonds, and SiF6 2− uses sp3 d2 hydrid orbitals to form six Si–F bonds. Furthermore, silicon can use its d orbitals to form dπ –pπ multiple bonds, whereas carbon only uses its p orbitals to form pπ –pπ multiple bonds. Trisilylamines such as N(SiH3 )3 is a planar molecule, as shown in Fig. 14.4.1(a), which differs from the pyramidal N(CH3 )3 molecule as shown in Fig. 14.4.1(b). In the planar configuration of N(SiH3 )3 , the central N atom uses trigonal planar spx py hybrid orbitals to form N–Si bonds, with the nonbonding electron pair of N residing in the 2pz orbital. Silicon has empty, relatively low-lying 3d orbitals able to interact appreciably with the 2pz orbital of the N atom. This additional delocalized pπ –dπ interaction shown in Fig 14.4.1(c) enhances the strength of the bonding that causes the NSi3 skeleton to adopt a planar configuration. (a)

(b)

(c)

Fig. 14.4.1.

(a) Structure of planar N(SiH3 )3 , (b) pyramidal N(CH3 )3 , and (c) the dπ–pπ bonding in N(SiH3 )3 . The occupied 2pz orbital of the N atom is shaded, and only one Si 3dxz orbital is shown for clarity.

534

Structural Chemistry of Selected Elements Table 14.4.1. Comparison of chemical bonds formed by C and Si

Bond

Bond length (pm)

Bond energy (kJ mol−1 )

C–C C–H C–O Si–Si Si–H Si–O

154 109 143 235 148 166

356 413 336 226 318 452

(3) Catenation and silanes The term catenation is used to describe the tendency for covalent bond formation between atoms of a given element to form chains, cycles, layers, or 3D frameworks. Catenation is common in carbon compounds, but it only occurs to a limited extent in silicon chemistry. The reason can be deduced from the data listed in Table 14.4.1. Inspection of Table 14.4.1 shows that E(C–C) > E(Si–Si), E(C–H) > E(Si– H) and E(C–C) > E(C–O), but E(Si–Si) y), including [Sn8 R4 ], [Sn8 R6 ]2− , [Sn9 R3 ], and [Sn10 R3 ]− , in which R represents a bulky aryl or silyl ligand, and their structures are displayed in Figs. 14.7.4(a)–(d), respectively. The largest tin clusters known to date are the pair of isoleptic amido complexes [Sn15 Z6 ] (Z = N(2,6-i Pr2 C6 H3 )(SiMe2 X); X = Me, Ph). Both

R [Si8R6];R = SitBu3

554

Structural Chemistry of Selected Elements possess a common polyhedral core consisting of fourteen tin atoms that fully encapsulates a central tin atom. The eight ligand-free peripheral tin atoms constitute the corners of a distorted cube, with each of its six faces capped by a Sn{N(2,6-i Pr2 C6 H3 )(SiMe2 X)} moiety, as shown in Fig. 14.7.4(e). The edges of the Sn14 polyhedron have an average length of 302 pm. The Sn(central)– Sn bonds in this high-nuclearity Sn@Sn14 metalloid cluster have an average length of 315 pm, which is close to the corresponding value of 310 pm in gray tin (α-Sn, diamond lattice) but considerably longer than that in white tin (β-Sn). Interestingly, the isoleptic compound Si8 R6 (R = Sit Bu3 ; “supersilyl”) does not exhibit a cubanoid cluster skeleton, but instead contains an unsubstituted Si2 dumbbell with a short Si–Si single bond of 229(1) pm, which is sandwiched between two almost parallel Si3 R3 rings, as illustrated in Fig. 14.7.4(f). Each terminal of the Si2 dumbbell acts as a bridgehead with an “inverted” tetrahedral bond configuration analogous to that found in 1-cyano-tetracyclodecane (see Section 14.3.5), forming two normal Si–Si bonds of 233 pm to one Si3 R3 ring and a longer one of 257 pm to the other. In the crystal structure, the atoms of the Si2 dumbbell are disordered over six sites. An intermetalloid cluster is a metalloid cluster composed of more than one metal, for example [Ni2 @Sn17 ]4− . Known intermetalloid clusters involving other Group 14 elements and various transition metals include [Pd2 @Ge18 ]4− , [Ni(Ni@Ge9 )2 ]4− , [Ni@Pb10 ]2− , and [Pt@Pb12 ]2− ; in the latter complex, the Pt atom is encapsulated by a Pb12 icosahedron (see Fig. 9.6.18).

14.7.5

Donor–acceptor complexes of Ge, Sn and Pb

The system R2 Sn→SnCl2 , with R = CH(SiMe3 )C9 H6 N), provides the first example of a stable donor–acceptor complex between two tin centers, as shown in Fig. 14.7.5. The alkyl ligand R is bonded in a C, N -chelating fashion to a Sn atom which adopts a pentacoordinate square-pyramidal geometry. This Sn atom is bonded directly to the other Sn atom of the SnCl2 fragment with a Sn– Sn distance of 296.1 pm, which is significantly longer than the similar distance of 276.8 pm in R2 Sn = SnR2 [R = CH(SiMe3 )2 ], and much shorter than the similar distance of 363.9 pm in Ar2 Sn–SnAr2 [Ar = 2,4,6-(CF3 )3 C6 H2 ]. The fold angle defined as the angle between the Sn–Sn vector and the SnCl2 plane is 83.3◦ . Some donor–acceptor complexes containing Ge–Ge and Sn–Sn bonds are listed in Table 14.7.2. The compounds listed in Table 14.7.2 have the formal formula: which indicate the presence of a M=M double bond, but the measured M–M bond lengths vary over a wide range. The M2 C4 (or M2 Si4 ) skeleton is not planar, in contrast with that of an olefin. Thus the properties of the formal M=M bonds are diverse and interesting. Two examples listed in this table are discussed below. As reference data, the “normal” values M–M single-bond lengths are calculated from the covalent radii (Table 3.4.3) and the “normal” bond lengths of M=M double bonds are estimated as 0.9 × (single-bond lengths). Thus the

Group 14 Elements (a)

555

(b)

N

83.3˚

Cl

Sn

Sn

Cl

CH

Me3Si

Sn

Sn

Me3Si

CH

Cl

Fig. 14.7.5.

N

Structure of the R2 Sn→SnCl2 (R = CH(SiMe3 )C9 H6 N). (a) Molecular structure (the SiMe3 groups have been omitted for clarity), (b) the lone pair forming a donor–acceptor bond.

N

“normal” bond lengths are Ge–Ge 244 pm, Ge = Ge 220 pm, Sn–Sn 280 pm, Sn = Sn 252 pm.

Compound A in Table 14.7.2, (Me3 SiN=PPh2 )2 C=Ge→Ge=C(Ph2 P= NSiMe3 )2 , comprises two germavinylidene units Ge=C(Ph2 P=NSiMe3 )2 bonded together in a head-to-head manner. The molecule is asymmetrical with

Table 14.7.2. Some donor–acceptor complexes with Ge–Ge and Sn–Sn bonds

Compound∗

M–M bond length (pm)

[Ge(2,6-Et2 C6 H3 )2 ]2 [Ge(2,6-i-C3 H7 )2 C6 H3 ]{2,4,6-Me3 C6 H2 }2 [Ge{CH(SiMe3 )2 }2 ]2 A [Sn{CH(SiMe3 )2 }2 ]2 [Sn{Si(SiMe3 )3 }2 ]2 [Sn(4,5,6-Me3 -2-t BuC6 H)2 ]2 B C [Sn{2,4,6-(CF3 )3 C6 H2 }2 ]2

Ge–Ge, 221.3 Ge–Ge, 230.1 Ge–Ge, 234.7 Ge–Ge, 248.3 Sn–Sn, 276.8 Sn–Sn, 282.5 Sn–Sn, 291.0 Sn–Sn, 300.9 Sn–Sn, 308.7 Sn–Sn, 363.9

*A

B Me3Si N

Me3Si N Ph2P Me3Si

Ge

Ph2 P C Ge

Me3Si N P Ph2

PPh2

Me3Si N

N

tBu

SiMe3 Sn

C N

C

tBu

Me3Si

N tBu

Me2N Me2N

Sn

tBu

NMe2

N SiMe3

CH2tBu N

Sn

Sn N

NMe2

CH2tBu

556

Structural Chemistry of Selected Elements (a)

(b) filled sp2 AO

Fig. 14.7.6.

Sn–Sn bonding model in [Sn{CH(SiMe3 )2 }2 ]2 : (a) overlap of atomic orbitals, (b) representation of the donor–acceptor bonding.

_ Sn R R

.. + + + ..+

empty 5p AO

R

R R

Sn

R

sp2 hybridized

Sn

_

Sn

R R

two different Ge environments: four-coordinate Ge and two-coordinate Ge, and shows trans linkage of the C=Ge–Ge=C skeleton, the torsion angle about the Ge–Ge axis being 43.9◦ . The Ge–Ge bond distance of 248.3 pm is consistent with a single bond, and both observed Ge–C bond lengths 190.5 and 190.8 pm are between those of standard Ge–C and Ge=C bonds. Therefore, the Ge–Ge bond in compound A is more approximately described as a donor–acceptor interaction similar to that of R2 Sn→SnCl2 (as shown in Fig. 14.7.5), and the four-coordinate Ge behaves as the donor and the two-coordinate Ge as a Lewis acid center. The compound [Sn{CH(SiMe3 )2 }2 ]2 does not possess a planar Sn2 C4 framework, and the Sn–Sn bond length (276.8 pm) is too long to be consistent with a “normal” double bond. A bonding model involving overlap of filled sp2 hybrids and vacant 5p atomic orbitals has been suggested, as shown in Fig. 14.7.6. The structure is similar to that in Fig. 14.4.7(e), but the trans-bent angle is larger. The digermanium alkyne analog 2,6-Dipp2 H3 C6 Ge≡GeC6 H3 -2,6-Dipp2 (Dipp = C6 H3 -2,6-i Pr2 ) was synthesized by the reaction of Ge(Cl)C6 H3 -2,6Dipp2 with potassium in THF or benzene. It was isolated as orange-red crystals and fully characterized by spectroscopic methods and X-ray crystallography. The digermyne molecule is centrosymmetric with a planar trans-bent C(ipso)– Ge–Ge–C(ipso) skeleton, and the central aryl ring of the terphenyl ligand is virtually coplanar with the molecular skeleton, each flanking aryl ring being oriented at ∼82◦ with respect to it. The structural parameters are C–Ge, 199.6 pm; Ge–Ge, 228.5 pm (considerably shorter than the Ge–Ge single-bond distance of approx. 244 pm); C–Ge–Ge, 128.67◦ . The measured Ge–Ge distance lies on the short side of the known range (221–46 pm) for digermenes, the digermanium analogs of alkenes. filled sp AO Fig. 14.7.7.

Ge–Ge bonding model in Ar, Ge≡GeAr, (Ar, =2,6-(C6 H3 -2,6-i Pr2 )2 C6 H3 ): (a) overlap of atomic orbitals, showing that donor–acceptor σ bonding occurs in the molecular plane, and (b) representation of the multiple bonding.

half-filled 4pz AO

_ Ar'

sp hybridized

+ Ge _

empty 4p AO

+ + +

+ Ge + _

_

Ar' Ar'

Ge

π

Ge

Ar'

By analogy to the model used to describe a Sn=Sn double bond, the observed geometry of the digermyne molecule and its multiple bonding character can be rationalized as shown in Fig. 14.7.7. Each germanium atom is considered to be sp hybridized in the C–Ge–Ge–C plane; a singly filled sp hybrid orbital is used to form a covalent bond with the terphenyl ligand, and the other sp hybrid is

Group 14 Elements completely filled and forms a donor bond with an empty in-plane 4p orbital on the other germanium atom. Two half-filled 4pz orbitals, one on each germanium atom and lying perpendicular to the molecular skeleton, then overlap to form a much weaker π bond. This simplified bonding description is consistent with the trans-bent molecular geometry and the fact that the formal Ge≡Ge bond length is not much shorter than that of the Ge=Ge bond. The distannyne Ar, SnSnAr, and diplumbyne Ar∗ PbPbAr∗ (Ar∗ = 2,4,6(C6 H3 -2,6-i Pr2 )3 C6 H2 ) have also been synthesized as crystalline solids and fully characterized. They are isostructural with digermyne, and their structural parameters are Sn–Sn, 266.75 pm; C–Sn–Sn, 125.24◦ ; Pb–Pb, 318.81 pm; C–Pb–Pb, 94.26◦ . Recent studies of the chemical reactivities of digermynes showed that it has considerable diradical character, which can be represented by a canonical form with an unpaired electron on each germanium atom, i.e., negligible overlap between the half-filled 4pz orbitals. The reactivity of the alkyne analogs decreases in the order Ge > Sn > Pb. In the diplumbyne, the Pb–Pb bond length is significantly longer than the value of approximately 290 pm normally found in organometallic lead–lead bonded species, e.g., Me3 PbPbMe3 . This suggests that a lone pair resides in the 6s orbital of each lead atom in the dilead compound, and a single σ bond results from head-to-head overlap of 6p orbitals. In summary, it is noted that multiple bonding between the heavier Group 14 elements E (Ge, Sn, Pb) differs in nature in comparison with the conventional σ and π covalent bonds in alkenes and alkynes. In an E=E bond, both components are of the donor–acceptor type, and a formal E≡E bond involves two donor– acceptor components plus a p–p π bond. There is also the complication that the bond order may be lowered when each E atom bears an unpaired electron or a lone pair. The simple bonding models provide a reasonable rationale for the marked difference in molecular geometries, as well as the gradation of bond properties in formally single, double and triple bonds, in compounds of carbon versus those of its heavier congeners.

References 1. J. March, Advanced Organic Chemistry, 4th edn., Wiley, New York, 1992. 2. N. N. Greenwood and A. Earnshaw, Chemistry of the Elements, 2nd edn., Butterworth-Heinemann, Oxford, 1997. 3. C. E. Housecroft and A. G. Sharpe, Inorganic Chemistry, 2nd edn., Prentice-Hall, Harlow, 2004. 4. D. F. Shriver, P. W. Atkins, T. L. Overton, J. P. Rourke, M. T. Weller and F. A. Armstrong, Inorganic Chemistry, 4th edn., Oxford University Press, Oxford, 2006. 5. F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, in A. J. C. Wilson (ed.), International Tables for Crystallography, vol. C, pp. 685–06, Kluwer Academic Publishers, Dordrecht, 1992. 6. J. Baggott, Perfect Symmetry, The Accidental Discovery of Buckminster Fullerene, Oxford University Press, Oxford, 1994. 7. H. W. Kroto, J. E. Fischer and D. E. Cox (eds.), Fullerenes, Pergamon Press, Oxford, 1993. 8. R. Taylor, Lecture Notes on Fullerene Chemistry: A Handbook for Chemists, Imperial College Press, London, 1999.

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Group 14 Elements 32. T. A. Murphy, T. Pawlik, A. Weidinger, M. Höhne, R. Alcala and J. M. Spaeth, Observation of atom-like nitrogen in nitrogen-implanted solid C60 . Phys. Rev. Lett. 77, 1075–78 (1996). 33. S. Stevenson, G. Rice, T. Glass, K. Harich, F. Cromer, M. R. Jordan, J. Craft, A. Hadju, R. Bible, M. M. Olmsted, K. Maitra, A. J. Fisher, A. L. Balch and H. C. Dorn, Small-bandgap endohedral metallofullerenes in high yield and purity. Nature 401, 55–7 (1999). 34. T. Murahashi, M. Fujimoto, M.-a. Oka, Y. Hashimoto, T. Uemura, Y. Tatsumi, Y. Nakao, A. Ikeda, S. Sakaki and H. Kurosawa, Discrete sandwich compounds of monolayer palladium sheets. Science 313, 1104–07 (2006). 35. F. Toda, Naphthocyclobutenes and benzodicyclobutadienes: synthesis in the solid state and anomalies in the bond lengths. Eur. J. Org. Chem. 1377–86 (2000). 36. O. T. Summerscales, F. G. N. Cloke, P. B. Hitchcock, J. C. Green and N. Hazari, Reductive cyclotrimerization of carbon monoxide to the deltate dianion by an organometallic uranium complex. Science 311, 829–31 (2006). 37. D. R. Huntley, G. Markopoulos, P. M. Donovan, L. T. Scott and R. Hoffmann, Squeezing C–C bonds. Angew. Chem. Int. Ed. 44, 7549–53 (2005). 38. F. R. Lemke, D. J. Szalda and R. M. Bullock, Ruthenium/zirconium complexes containing C2 bridges with bond orders of 3, 2, and 1. Synthesis and structures of Cp(PMe3 )2 RuCHn CHn ZrClCp2 (n = 0, 1, 2). J. Am. Chem. Soc. 113, 8466–77 (1991). 39. U. Ruschewitz, Binary and ternary carbides of alkali and alkaline-earth metals. Coord. Chem. Rev. 244, 115–36 (2003). 40. G.-C. Guo, G.-D. Zhou and T. C. W. Mak, Structural variation in novel double salts of silver acetylide with silver nitrate: fully encapsulated acetylide dianion in different polyhedral silver cages. J. Am. Chem. Soc. 121, 3136–41 (1999). 41. H.-B. Song, Q.-M. Wang, Z.-Z. Zhang and T. C. W. Mak, A novel luminescent copper(I) complex containing an acetylenediide-bridged, butterfly-shaped tetranuclear core. Chem. Commun., 1658–59 (2001). 42. K. C. Kim, C. A. Reed, D. W. Elliott, L. J. Mueller, F. Tham and J. B. Lambert, Crystallographic evidence for a free silylium Ion. Science 297, 825–7 (2002). 43. A. Sekiguchi and H. Sakurai, Cage and cluster compounds of silicon, germanium and tin. Adv. Organometal. Chem. 45, 1–38 (1995). 44. A. Sekiguchi, S. Inoue, M. Ichinoche and Y. Arai, Isolable anion radical of blue disilene (t Bu2 MeSi)2 Si=Si(SiMet Bu2 )2 formed upon one-electron reduction: synthesis and characterization. J. Am. Chem. Soc. 126, 9626–29 (2004). 45. S. Nagase, Polyhedral compounds of the heavier group 14 elements: silicon, germanium, tin and lead. Acc. Chem. Res. 28, 469–76 (1995). 46. M. Brynda, R. Herber, P. B. Hitchcock, M. F. Lappert, I. Nowik, P. P. Power, A. V. Protchenko, A. Ruzicka and J. Steiner, Higher-nuclearity group 14 metalloid clusters: [Sn9 {Sn(NRR,)}6 ]. Angew. Chem. Int. Ed. 45, 4333–37 (2006). 47. G. Fischer, V. Huch, P. Maeyer, S. K. Vasisht, M. Veith and N. Wiberg, Si8 (Sit Bu3 )6 : a hitherto unknown cluster structure in silicon chemistry. Angew. Chem. Int. Ed. 44, 7884–87 (2005). 48. W. P. Leung, Z. X. Wang, H. W. Li and T. C. W. Mak, Bis(germavinylidene)[(Me3 SiN=PPh2 )2 C=Ge→ Ge=C(Ph2 P=NSiMe3 )] and 1,3-dimetallacyclobutanes [M{µ2 -C(Ph2 PSiMe3 )2 }]2 (M = Sn, Pb). Angew. Chem. Int. Ed. 40, 2501–3 (2001). 49. W. P. Leung, W. H. Kwok, F. Xue and T. C. W. Mak, Synthesis and crystal structure of an unprecedented tin(II)-tin(II) donor-acceptor complex, R2 Sn→SnCl2 , [R=CH(SiMe3 )C9 H6 N-8]. J. Am. Chem. Soc. 119, 1145–46 (1997).

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Structural Chemistry of Group 15 Elements

15.1

The N2 molecule, all-nitrogen ions and dinitrogen complexes

15.1.1

The N2 molecule

Nitrogen is the most abundant uncombined element in the earth’s surface. It is one of the four essential elements (C, H, O, N) that support all forms of life. It constitutes, on the average, about 15% by weight in proteins. The industrial fixation of nitrogen in the production of agricultural fertilizers and other chemical products is now carried out on a vast scale. The formation of a triple bond, N≡N, comprising one σ and two π components with bond length 109.7 pm, accounts for the extraordinary stability of the dinitrogen molecule N2 ; the energy level diagram for N2 is shown in Fig. 3.3.3(a). Gaseous N2 is rather inert at room temperature mainly because of the great strength of the N≡N bond and the large energy gap between the HOMO and LUMO (∼8.6 eV), as well as the absence of bond polarity. The high bond dissociation energy of the N2 molecule, 945 kJ mol−1 , accounts for the following phenomena: (a) Molecular nitrogen constitutes 78.1% by volume (about 75.5% by weight) of the earth’s atmosphere. (b) It is difficult to “fix” nitrogen, i.e., to convert molecular nitrogen into other nitrogen compounds by means of chemical reactions. (c) Chemical reactions that release N2 as a product are highly exothermic and often explosive. 15.1.2

Nitrogen ions and catenation of nitrogen

There are three molecular ions which consist of nitrogen atoms only. (1) Nitride ion N3− The N3− ion exists in salt-like nitrides of the types M3 N and M3 N2 . In M3 N compounds, M is an element of group 1 (Li) or Group 11 (Cu, Ag). In M3 N2 compounds, M is an element of group 2 (Be, Mg, Ca, Sr, Ba) or Group 12 (Zn, Cd, Hg). In these compounds, the bonding interactions between N and M atoms are essentially ionic, and the radius of N3− is 146 pm. Nitride Li3 N exhibits

15

562

Structural Chemistry of Selected Elements high ionic conductivity with Li+ as the current carrier. The crystal structure of Li3 N has been discussed in Section 12.2. (2) Azide N− 3

The azide ion N− 3 is a symmetrical linear group that can be formed by neutralization of hydrogen azide HN3 with alkalis. The bent configuration of HN3 is shown below: H 98 pm

114˚ N

N N 124 pm 113 pm

The Group 1 and 2 azides NaN3 , KN3 , Sr(N3 )2 and Ba(N3 )2 are wellcharacterized colorless crystalline salts which can be melted with little decomposition. The corresponding Group 11 and 12 metal azides such as AgN3 , Cu(N3 )2 and Pb(N3 )2 , are shock-sensitive and detonate readily, and they are far less ionic with more complex structures. The salt (PPh4 )+ (N3 HN3 )− has been synthesized from the reaction of Me3 SiN3 with (PPh4 )(N3 ) in ethanol; the (N3 HN3 )− anion has a nonplanar bent structure consisting of distinct N− 3 and HN3 units connected by a hydrogen bond, as shown in Fig. 15.1.1(a). In Cu2 (N3 )2 (PPh3 )4 and [Pd2 (N3 )6 ]2− , N− 3 acts either as a terminal or a bridging ligand, as shown in Figs. 15.1.1(b) and (c), respectively. The azide ion N− 3 can also be combined with a metalloid ion such as As5+ to form [As(N3 )6 ]− , as shown in Fig. 15.1.1(d). Table 15.1.1 lists the coordination modes of N− 3 in its metal complexes; the highest-ligation µ-1,1,1,3,3,3 mode (h) was found to exist in the double salt AgN3 ·2AgNO3 . The uranium(IV) heptaazide anion U(N3 )3− 7 has been synthesized as the n-tetrabutylammonium salt. This is the first homoleptic azide of an actinide (a)

(b) Ph3P 272 pm

Cu

Cu

Ph3P

PPh3

N N N

N N N

PPh3

118 pm (c)

(d) 2–

N

–

N N

N N N Pd Fig. 15.1.1.

Structures of some azide compounds: (a) (N3 HN3 )− , (b) Cu(N3 )2 (PPh3 )4 , (c) [Pd2 (N3 )6 ]2− , and (d) [As(N3 )6 ]− .

N N N

N N N Pd

N N N N 122 pm N 114 pm N

As

N

Group 15 Elements

563

− Table 15.1.1. Coordination modes of N3 in metal complexes

M

N

N

N

M

N

N

(a)

N

M

N

(c)

M N

N

N

M

M

M N

N

N

M

M N

M (e)

N

N

N

M

(d) M M N M

N M

(b)

M

N

M

M

N M

(f) M M N M

N

N

M M M

(h)

(g)

as well as the first structurally characterized heptaazide. Two polymorphs of (Bu4 N)3 [U(N3 )7 ] were obtained from crystallization in CH3 CN/CFCl3 (form A) or CH3 CH2 CN (form B). FormAbelongs to space group Pa3¯ with Z = 8, and hence the U atom and one of the three independent azide groups are located on a crystallographic 3-axis. This results in a 1:3:3 monocapped octahedral arrangement of the azide ligands around the central uranium atom, as illustrated in Fig. 15.1.2(a). Form B crystallizes in space group P21 /c with Z = 4, and the azide ligands exhibit a distorted 1:5:1 pentagonal-bipyramidal coordination mode, as shown in Fig. 15.1.2(b). The U–Nα bond lengths range from 232 to 243 pm. Two isomeric polymorphs of [(C5 Me5 )2 U(µ-N)U(µ-N3 )(C5 Me5 )2 ]4 have been synthesized and structurally characterized by X-ray crystallography. In the tetrameric macrocycle, eight (η5 -C5 Me5 )2 U2+ units are charge-balanced 3− (nitride) ligands. Isomer A by four N− 3 (azide) ligands and four formally N has a (UNUN3 )4 ring in a pseudo-crown (or chair) conformation, whereas that of isomer B exhibits a pseudo-saddle (or boat) geometry, as shown in Fig. 15.1.3. The observed U–N(azide) bond distances in the range 246.7-252.5 pm are longer than typical U(IV)–N single bonds. The U–N(nitride) bond lengths in the range (a)

(b)

Fig. 15.1.2.

Molecular structure of U(N3 )3− 7 in (a) form A and (b) form B of the Bu4 N+ salt. [Ref. M.-J. Crawford, A. Ellern and P. Meyer, Angew. Chem. Int. Ed. 44, 7874–78 (2005).]

564

Structural Chemistry of Selected Elements

Fig. 15.1.3.

Molecular skeleton of the (UNUN3 )4 ring in two crystalline polymorphs of [(C5 Me5 )2 U(µ-N)U(µN3 )(C5 Me5 )2 ]4 : pseudo-crown conformation observed for isomeric form A and pseudo-saddle observed for form B. The pair of η5 -C5 Me5 groups bonded to each uranium(IV) atom is not shown. From W. J. Evans, S. A. Kozimor and J. W. Ziller, Science 309, 1835–8 (2005).

A

B

204.7-209.0 pm are consistent with a bond order of 2 in a symmetrical bonding scheme for each UNU segment, rather than an alternating single-triple-bond pattern, as shown below: U

N

U

U

N

U

symmetrical nitride bridging

U

N

U

asymmetrical nitride bridging

(3) Pentanitrogen cation N5 + The pentanitrogen cation N+ 5 was first synthesized in 1999 as the white solid N5 +AsF6 − , which is not very soluble in anhydrous HF but stable at −78◦ C. The N+ 5 cation has a closed-shell singlet ground state, and its C2v symmetry was characterized by Raman spectroscopy and NMR of 14 N and 15 N nuclei. A series − of 1:1 salts of N+ 5 have also been prepared with the monoanions HF2 (as the + − − − − − − adduct N5 HF2 · nHF), BF4 , PF6 , SO3 F , (Sb2 F11 ) , B(N3 )4 and P(N3 )− 6. − , which is stable at (Sb F ) A determination of the crystal structure of N+ 2 11 5 room temperature, yielded the structural parameters shown in Fig. 15.1.4. Note that each terminal N–N–N segment in N+ 5 deviates from exact linearity. A description of the bonding in this cation is given in Chapter 5, Section 5.8.3. The catenation of nitrogen refers to the tendency of N atoms to be connected to each other, and is far lower than those of C and P. This is because the repulsion of lone pairs on adjacent N atoms weakens the N–N single bond, and the lone pairs can easily react with electrophilic species. The structures and examples of known compounds that contain chains and rings of N atoms are listed in Table 15.1.2. Note that none of these has a linear configuration of nitrogen atoms. +

168˚

Fig. 15.1.4.

Molecular dimensions of the pentanitrogen cation N+ 5 from crystal structure analysis.

130 pm 111˚

15.1.3

111 pm

Dinitrogen complexes

Molecular nitrogen can react directly with some transition-metal compounds to form dinitrogen complexes, the structure and properties of which are of considerable interest because they may serve as models for biological nitrogen

Group 15 Elements Table 15.1.2. Species containing catenated N atoms

Number of N atoms 3 3 4 4 5 6 8 5

Chain or ring

Example

[N–N–N]+ N–N=N N–N=N–N N–N–N–N N=N–N–N=N N=N–N–N–N=N N=N–N–N=N–N–N=N

[H2 NNMe2 NH2 ]Cl MeHN–N=NH H2 N–N=N–NH2 , Me2 N–N=N–NMe2 (CF3 )2 N–N(CF3 )–N(CF3 )–N(CF3 )2 PhN=N–N(Me)–N=NPh PhN=N–N(Ph)–N(Ph)–N=NPh PhN=N–N(Ph)–N=N–N(Ph)–N=NPh

N N N N

N

N N N N

N Ph

fixation and as intermediates in synthetic applications. The known coordination modes of dinitrogen are discussed below and summarized in Table 15.1.3. The skeletal views of dinitrogen coordination modes in some metal complexes are shown in Fig. 15.1.5. (1) η1 -N2 The first complex containing molecular nitrogen as a ligand, [Ru(NH3 )5 (N2 )]Cl2 , was synthesized and identified in 1965 [Fig. 15.1.5(a)]. The complex (Et2 PCH2 CH2 PEt2 )2 Fe(N2 ) exhibits trigonal bipyramidal coordination geometry, with N2 lying in the equatorial plane, as shown in Fig. 15.1.5(a, ). Most examples of stable dinitrogen complexes have been found to belong to the η1 – N2 category, in which the dinitrogen ligand binds in a linear, end-on mode with only a slightly elongated N–N bond length (112–24 pm) as compared to that in gaseous dinitrogen (109.7 pm). The stable monomeric titanocene complexes {(PhMe2 Si)C5 H4 }2 TiX (X = N2 , CO) are isomorphous, with a crystallographic C2 axis passing through the Ti atom and the η1 –X ligand. The measured bond distances (in pm) are Ti–N = 201.6(1), N–N = 111.9(2) for the dinitrogen complex, and Ti–C = 197.9(2), C–O = 115.1(2) for the carbonyl complex. (2) µ-(bis-η1 )-N2 As a bridging ligand in dinuclear systems, dinitrogen may formally be classified into three types. (a) M–N≡N–M: This dinitrogen ligand corresponds to a neutral N2 molecule, which uses its lone pairs to coordinate to two M atoms. Complexes of this type show a relatively short N–N distance of 112–20 pm. In [(η5 -C5 Me5 )2 Ti]2 (N2 ), the binuclear molecular skeleton consists of two (η5 -C5 Me5 )2 Ti moieties bridged by the N2 ligand in an essentially linear Ti–N≡N–Ti arrangement, as shown in Fig. 15.1.5(b). The N–N distance is 116 pm (av.). (b) M=N=N=M: This dinitrogen ligand corresponds to diazenido(-2). The (N2 )2− anion coordinates to two M atoms. In (Mes)3 Mo(N2 )Mo(Mes)3

565

566

Structural Chemistry of Selected Elements (where Mes = 2,4,6-Me3 C6 H2 ), Mo=N=N=Mo forms a linear chain. The length of the N–N distance is 124.3 pm. (c) M≡N–N≡M: This dinitrogen ligand corresponds to hydrazido(-4). The (N2 )4− anion coordinates to two M atoms. In [PhP(CH2 SiMe2 NPh2 )2 NbCl]2 (N2 ), the Nb pm.

N–N

Nb moiety is linear, and the distance of N–N is 123.7

(3) µ3 -η1 : η1 : η2 -N2 In the [(C10 H8 )(C5 H5 )2 Ti2 ](µ3 –N2 )[(C5 H4 )(C5 H5 )3 Ti2 ] complex, the dinitrogen ligand is coordinated simultaneously to three Ti atoms, as shown in Fig. 15.1.5(c). The N–N distance is 130.1 pm. (4) µ3 -η1 : η1 : η1 -N2 In the mixed-metal complex [WCl(py)(PMePh)3 (µ3 -N2 )]2 (AlCl2 )2 , both WNN linkages are essentially linear, and the four metal atoms and two µ3 –N2 ligands almost lie in the same plane, as shown in Fig. 15.1.5(d). (5) µ-(η1 : η2 )-N2 In [PhP(CH2 SiMe2 NPh)2 ]2 Ta2 (µ-H)2 (N2 ), the dinitrogen moiety is end-on bound to one Ta atom and side-on bound to the other, as shown in Fig. 15.1.5(e). The N–N distance of 131.9 pm is consistent with a formal assignment of the bridging dinitrogen moiety as (N2 )4− . The shortest distance of the end-on Ta– N bond is 188.7 pm, which is consistent with its considerable double-bond character. (6) µ-(bis-η2 )-N2 (planar) Figure 15.1.5(f) shows a planar, side-on bonded N2 ligand between two Zr atoms in the compound [Cp,, 2 Zr]2 (N2 ) [Cp,, = 1,3-(SiMe2 )2 C5 H3 ]. The N–N bond length is 147 pm. Side-on coordination of the dinitrogen ligand appears to be important for its reduction. (7) µ-(bis-η2 )-N2 (nonplanar) In the compound Li{[(SiMe3 )2 N]2 Ti(N2 )}2 , each Ti atom is side-on bound to two N2 molecules, as shown in Fig. 15.1.5(g). The N–N distance is 137.9 pm. (8) µ4 -η1 : η1 : η2 : η2 -N2 In [Ph2 C(C4 H3 N)2 Sm]4 (N2 ), the N2 moiety is end-on bound to two Sm atoms and side-on bound to the other two, as shown in Fig. 15.1.5(h). The bond lengths are: N–N 141.2 pm, Sm(terminal)–N 217.7 pm and Sm(bridging)–N 232.7 pm. (9) µ5 -η1 : η1 : η2 : η2 : η2 -N2 In {[(–CH2 –)5 ]4 calixtetrapyrrole}2 Sm3 Li2 (N2 )[Li(THF)2 ]·(THF), the N2 moiety is end-on bound to two Li atoms and side-on bound to three Sm atoms, as shown in Fig. 15.1.5(i). The bond lengths are N–N 150.2 pm, Sm–N 233.3 pm(av.), and Li–N 191.0 pm(av.).

Group 15 Elements

567

Table 15.1.3. Coordination modes of dinitrogen

Coordination mode

Example

dN−N (pm)

Structure in Fig.15.1.5

[Ru(NH3 )5 (N2 )]2+

112

(a)

(depe)2 Fe(N2 )

113.9

(a,)

[(C5 Me5 )2 Ti]2 (N2 )

116 (av.)

(b)

(Mes)3 Mo(N2 )Mo(Mes)3 [PhP(CH2 SiMe2 NPh2 )2 NbCl]2 (N2 )

124.3 123.7

[(C10 H8 )(C5 H5 )2 Ti2 ][(C5 H4 )(C5 H5 )3 Ti2 ](N2 )

130.1

(c)

[WCl(py)(PMePh)3 (N2 )]2 (AlCl2 )2

125

(d)

[PhP(CH2 SiMe2 NPh)2 ]2 Ta2 (µ-H)2 (N2 )

131.9

(e)

[Cp,, 2 Zr]2 (N2 )

147

(f)

Li{[(SiMe3 )2 N]2 Ti(N2 )}2

137.9

(g)

[Ph2 C(C4 H3 N)2 Sm]4 (N2 )

141.2

(h)

{[(–CH2 –)5 ]4 calixtetrapyrrole}2 Sm3 Li2 (N2 )

150.2

(i)

[(THF)2 Li(OEPG)Sm]2 Li4 (N2 )

152.5

( j)

568

Structural Chemistry of Selected Elements (a')

(a) Ru

N

(b) Fe

N

N

(c)

Ti

(d)

N N (e)

W

Al

Ti (f)

(g)

Ta N

N

(h)

Zr N

(i)

N

Sm

Ti (j)

N Sm

Li

N

Li

Sm

Fig. 15.1.5.

Dinitrogen coordination modes in metal complexes.

(10) µ6 -η1 : η1 : η2 : η2 : η2 : η2 -N2 In [(THF)2 Li(OEPG)Sm]2 Li4 (N2 ) (OEPG = octaethylporphyrinogen), the N2 moiety is end-on bound to two Li atoms and side-on bound to two Sm atoms and two Li atoms, as shown in Fig. 15.1.5(j). The bond lengths are N–N 152.5 pm, Sm–N 235.0 pm (av.), and Li–N 195.5 pm(av.). The bonding of dinitrogen to transition metals may be divided into the “endon” and “side-on” categories. In the end-on arrangement, the coordination of the N2 ligand is accomplished by a σ bond between the 2σg orbital of the nitrogen molecule and a hybrid orbital of the metal, and by π back-bonding from a doubly degenerate metal dπ orbitals (dxz , dyz ) to the vacant 1πg∗ orbitals (π∗xz , π∗yz ) of the nitrogen molecule, as shown in Fig. 15.1.6. In the side-on arrangement, the bonding is considered to arise from two interdependent components. In the first part, σ overlap between the filled π orbital of N2 and a suitably directed vacant hybrid metal orbital forms a donor bond. In the second part, the M atom and N2 molecule are involved in two back-bonding interactions, one having π symmetry as shown in Fig. 15.1.7(a), and the other with δ symmetry as shown in Fig. 15.1.7(b). These π and δ-back bonds synergically reinforce the σ bond.

Group 15 Elements

569

x M

N

N

z

Fig. 15.1.6.

Orbital interactions of N2 and transition-metal M in end-on coordinated dinitrogen complexes. The dπ-1π*g overlap shown here also occurs in the yz plane.

y π*xz

dxz

Since the overlap of a δ bond should be less effective than that of a π bond, the end-on mode is generally preferred over the side-on form. The transition-metal dinitrogen complexes have been investigated theoretically, and the results lead to the following generalizations: (a) Both σ donation and π or δ back donation are related to the formation of the metal-nitrogen bond, the former interaction being more important. (b) The N–N bond of the side-on complex is appreciably weakened by electron donation from the bonding π and σ orbitals of the N2 ligand to the vacant orbitals of the metal. (c) The end-on coordination mode takes precedence over the side-on one. The weak N–N bond in the side-on complex indicates that the N2 ligand in this type of compound is fairly reactive. The reduction of the coordinated nitrogen molecule may proceed through this activated form. (a)

(b) –

+ M

+

+

–

+

–

+

N –

+

–

–

M

z

N +

π*xz

dxz

x

N

N +

–

σ and π

15.2

Compounds of nitrogen

15.2.1

Molecular nitrogen oxides

–

–

+

+

y

π*xz

dxz δ

Nitrogen displays nine oxidation states ranging from −3 to +5. Since it is less electronegative than oxygen, nitrogen forms oxides and oxidized compounds with an oxidation number between +1 and +5. Eight oxides of nitrogen, N2 O, NO, N2 O2 , N2 O3 , NO2 , N2 O4 , N2 O5 and N4 O, are known, and the ninth, NO3 , exists as an unstable intermediate in various reactions involving nitrogen oxides. Their structures and some properties are presented in Table 15.2.1 and Fig. 15.2.1. All nitrogen oxides have planar structures. Nitrogen displays all its positive oxidation states in these compounds, and in N2 O, N2 O3 and N4 O the N atoms in

Fig. 15.1.7.

Orbital interactions of N2 and transition-metal M in side-on coordinate dinitrogen complexes.

570

Structural Chemistry of Selected Elements

Table 15.2.1. Structure and properties of the nitrogen oxides

Structure (in Fig.15.2.1)

'Hf0 (kJ mol−1 )

Properties

+1 or (0,+2)

(a) linear C∞v

82.0

+2

(b) linear C∞v

90.2

mp 182.4 K, bp 184.7 K, colorless gas, fairly unreactive with pleasuring odor and sweet taste mp 109 K, bp 121.4 K, colorless, paramagnetic gas

+2

(c), (d)

—

(e) planar Cs

80.2

+4

(f) C2v

33.2

Dinitrogen tetroxide

+4

(g) planar D2h

9.16

N2 O5

Dinitrogen pentoxide

+5

(h) planar C2v

11.3 (gas) −43.1 (cryst.)

N4 O

Nitrosyl azide

∗

(i) planar Cs

−297.3

Formula

Name

N2 O

N2 O3

Dinitrogen monoxide (dinitrogen oxide, nitrous oxide, laughing gas) Nitrogen oxide (nitric oxide, nitrogen monoxide) Dimer of nitrogen oxide Dinitrogen trioxide

NO2

Nitrogen dioxide

N2 O4

NO

(NO)2

Oxidation number

+3 or (+2,+4)

— mp 172.6 K, dec. 276.7 K, dark blue liquid, pale blue solid, reversibly dissociates to NO and NO2 orange brown, paramagnetic gas, reactive mp 262.0 K, bp 294.3 K, colorless liquid, reversibly dissociates to NO2 sublimes at 305.4 K, colorless, volatile solid consisting of − NO+ 2 and NO3 ; exists as N2 O5 in gaseous state pale yellow solid (188 K)

∗ The assignment of an oxidation number is not appropriate as only one of the four nitrogen atoms is bonded to the oxygen atom in the N O 4

molecule.

molecule have different oxidation states. In the gaseous state, six stable nitrogen oxides exist, each with a positive heat of formation primarily because the N≡N bond is so strong. The structure and properties of nitrogen oxides are presented in Table 15.2.1. (a)

(b) 113

119

(c) 115

115

(d) 223.7

218

(e) 114

(f) 119

186.9

(g)

127.0

(h)

(i)

Fig. 15.2.1.

Structure of nitrogen oxides (bond length in pm): (a) N2 O, (b) NO, (c) N2 O2 (in crystal), (d) N2 O2 (in gas), (e) N2 O3 , (f) NO2 , (g) N2 O4 , (h) N2 O5 , (i) N4 O.

121

175

115.4

134˚

122

134˚

133˚

119 150

110.5 120.4

Group 15 Elements (1) N2 O Dinitrogen oxide (nitrous oxide), N2 O, is a linear unsymmetrical molecule with a structure similar to its isoelectronic analog CO2 : −

+

+

−

N ← N = O ←→ N ≡ N − O . Dinitrogen oxide is unstable and undergoes dissociation when heated to about 870 K: N2 O −→ N2 + 1/2O2 . The activation energy for this process is high (∼520 kJ mol−1 ), so N2 O is relatively unreactive at room temperature. Dinitrogen oxide has a pleasant odor and sweet taste, and its past use as an anaesthetic with undesirable side effect accounts for its common name as “laughing gas.” (2) NO and (NO)2 The simplest thermally stable odd-electron molecule known is nitrogen monoxide, NO, which is discussed in the next section. High-purity nitrogen monoxide partially dimerizes when it liquefies to give a colorless liquid. The heat of dissociation of the dimer is 15.5 kJ mol−1 . The structure of the (NO)2 dimer in the crystalline and vapor states are shown in Figs. 15.2.1(c) and 15.2.1(d), respectively. The (NO)2 dimer adopts the cis arrangement with C2v symmetry. In the crystalline state, the N–N distance is 218 pm (223.7 pm in the gas phase), and the O· · ·O distance is 262 pm. The very long N–N distance has not been accounted for satisfactorily in bonding models. (3) N2 O3 Dinitrogen trioxide is formed by the reaction of stoichiometric quantities of NO and O2 : 2NO + 1/2O2 → N2 O3 . At temperatures below 172.6 K, N2 O3 crystallizes as a pale blue solid. On melting it forms an intensely blue liquid which, as the temperature is raised, is increasingly dissociated into NO and an equilibrium mixture of NO2 and N2 O4 . This dissociation occurs significantly above 243 K and the liquid assumes a greenish hue resulting from the brown color of NO2 mixed with the blue. The N–N distance of the N2 O3 molecule, 186.9 pm, is considerably longer than the typical N–N single bond (145 pm) in hydrazine, H2 N–NH2 . (4) NO2 and N2 O4 Nitrogen dioxide and dinitrogen tetroxide are in rapid equilibrium that is highly dependent on temperature. Below the melting point (262.0 K) the oxide consists entirely of colorless, diamagnetic N2 O4 molecules. As the temperature is raised to the boiling point (294.3 K), the liquid changes to an intense red-brown

571

572

Structural Chemistry of Selected Elements colored, highly paramagnetic phase containing 0.1% NO2 . At 373 K, the proportion of NO2 increases to 90%. The configuration, bond distances, and bond angles of NO2 and N2 O4 are given in Figs. 15.2.1(f) and 15.2.1(g). In view of the large bond angle of NO2 and its tendency for dimerization, bonding in the molecule can be described in terms of resonance between the following canonical structures:

N

N O

O

O

N O

N O

O

O

O

The N–N distance in planar N2 O4 is 175 pm, with a rotation barrier of about 9.6 kJ mol−1 . Although the N–N bond is of the σ type, it is lengthened because the bonding electron pair is delocalized over the entire N2 O4 molecule with a large repulsion between the doubly occupied MOs on the two N atoms. (5) N2 O5 and NO3 Nitrogen pentoxide, N2 O5 , is a colorless, light- and heat-sensitive crystalline − compound that consists of linear NO+ 2 cations (N–O 115.4 pm) and planar NO3 anions (N–O 124 pm). In the gas phase N2 O5 is molecular but its configuration and dimensions have not been reliably measured. Also, N2 O5 is the anhydride of nitric acid and can be obtained by carefully dehydrating the concentrated acid with P4 O10 at low temperatures: −10◦ C

4HNO3 + P4 O10 −−−→ 2N2 O5 + 4HPO3 . The existence of the fugitive, paramagnetic trioxide NO3 is also implicated in the N2 O5 -catalyzed decomposition of ozone, and its concentration is sufficiently high for its absorption spectrum to be recorded. It has not been isolated as a pure compound, but probably has a symmetrical planar structure like that of NO− 3. (6) N4 O Nitrosyl azide, N4 O, is a pale yellow solid formed by the reaction of activated, anhydrous NaN3 and NOCl, followed by low-temperature vacuum sublimation. The Raman spectrum and ab initio calculation characterized the structure of N4 O as that shown in Fig. 15.2.1(i). The bonding in the N4 O molecule can be represented by the following resonance structures:

N

+ – N .. N

.. N O

N

+ N

.. N N ..

–

O

– N

+ N

.. N N ..

O

Group 15 Elements (7) Molecule of the year for 1992: nitric oxide Nitric oxide, NO, was named molecule of the year for 1992 by the journal Science. It is one of the most extensively investigated molecules in inorganic and bioinorganic chemistry. Nitric oxide is biosynthesized in animal species, and its polarity and small molecular dimensions allow it to readily diffuse through cell walls, acting as a messenger molecule in biological systems. It plays an important role in the normal maintenance of many important physiological functions, including neurotransmission, blood clotting, regulation of blood pressure, muscle relaxation, and annihilation of cancer cells. The valence shell electron configuration of NO in its ground state is (1σ)2 (1σ∗ )2 (1π)4 (2σ)2 (1π∗ )1 , which accounts for the following properties: (a) The NO molecule has a net bond order of 2.5, bond energy 627.5 kJ mol−1 , bond length 115 pm, and an infrared stretching frequency of 1840 cm−1 . (b) The molecule is paramagnetic in view of its unpaired π∗ electron. (c) NO has a much lower ionization energy (891 kJ mol−1 or 9.23 eV) than N2 (15.6 eV) or O2 (12.1 eV). (d) NO has a dipole moment of 0.554 × 10−30 C m, or 0.166 Debye. (e) Employing its lone-pair electrons, NO serves as a terminal or bridging ligand in forming numerous coordination compounds. (f) NO is thermodynamically unstable ('G o = 86.57 kJ mol−1 , 'S o = 217.32 kJ mol−1 K−1 ) and decomposes to N2 and O2 at high temperature. It is capable of undergoing a variety of redox reactions. The electrochemical oxidation of NO around 1.0 V has been used to devise NO-selective amperometric microprobe electrodes to detect its release in biological tissues. As a result of its unique structure and properties, the NO molecule exhibits a wide variety of reactions with various chemical species. In particular, it readily releases an electron in the antibonding π∗ orbital to form the stable nitrosyl cation NO+ , increasing the bond order from 2.5 to 3.0, so that the bond distance decreases by 9 pm. The NO species in an aqueous solution of nitrous acid, HONO, is NO+ : HONO + H+ −→ NO+ + H2 O. There are many nitrosyl salts, including (NO)HSO4 , (NO)ClO4 , (NO)BF4 , (NO)FeCl4 , (NO)AsF6 , (NO)PtF6 , (NO)PtCl6 , and (NO)N3 . Nitrosyl halides are formed when NO reacts with F2 , Cl2 , and Br2 , and they all have a bent structure: N X

O

X = F, X–N 152 pm, N=O 114 pm, X–N=O 110◦ X = Cl, X–N 197 pm, N=O 114 pm, X–N=O 113◦ X = Br, X–N 213 pm, N=O 114 pm, X–N=O 117◦

573

574

Structural Chemistry of Selected Elements Because of its close resemblance to O2 and its paramagnetism, NO has been used extensively as an O2 surrogate to probe the metal environment of various metalloproteins. In particular, NO has been shown to bind to Fe2+ in heme-containing oxygen-transporting proteins, in a fashion nearly identical to O2 , with the important consequence of rendering the complex paramagnetic and thus detectable by EPR spectroscopy. Since the unpaired electron assumes appreciable iron d-orbital character, analysis of the EPR characteristics of hemo–protein nitrosyl complexes yields valuable information on both the ligand-binding environment around the heme and on the conformational state of the protein. Nitric oxide can bind to metals in both terminal and bridging modes to give metal nitrosyl complexes. Depending upon the stereochemistry of the complexes, NO may exhibit within one given complex either NO+ or NO− character, as illustrated in Table 15.2.2. Nitric oxide contains one more electron than CO and generally behaves as a three-electron donor in metal nitrosyl complexes. Formally this may be regarded as the transfer of one electron to the metal atom, thereby reducing its oxidation state by one, followed by coordination of the resulting NO+ to the metal atom as a two-electron donor. This is in accordance with the general rule that three terminal CO groups in a metal carbonyl compound may be replaced by two NO groups. In this type of bonding the M–N–O bond angle would formally be 180◦ . However, in many instances this bond angle is somewhat less than 180◦ , and slight bent M–N–O groups with angles in the range 165◦ to 180◦ are frequently found. In a second type of bonding in nitrosyl coordination compounds, the M–N–O bond angle lies in the range of 120◦ to 140◦ and the NO molecule acts as a oneelectron donor. Here the situation is analogous to XNO compounds and the M–N bond order is one. It should be emphasized that the NO+ and NO− “character” of NO and the linear or bent angle in a nitrosyl complex do not necessarily imply that NO would be released from the complex in the free form NO or as NO+ or NO− .

Table 15.2.2. Two types of MNO coordination geometry.

M

M–N–O Bond angle M–N distance NO frequency Chemical properties

165◦ – 180◦ ∼ 160 pm 1650 – 1985 cm−1 Electrophilic; NO+ similar to CO:

– + M =N = O Ligand behavior

three-electron donor

N

O

120◦ – 140◦ > 180 pm 1525 – 1590 cm−1 Nucleophilic; NO− similar to O2 :

M

N

O one-electron donor

Group 15 Elements Table 15.2.3. Oxo-acids of nitrogen

Formula

Name

Properties

HON=NOH Hyponitrous acid Weak acid; salts are known H2 NNO2 HNO H2 N2 O3 HNO2 HNO3 H3 NO4

15.2.2

Nitramide Nitroxyl Hyponitric acid Nitrous acid Nitric acid Orthonitric acid

Structure trans form, Fig. 15.2.3 (a) Fig. 15.2.2 (a) Fig. 15.2.2 (b)

Isomeric with hyponitrous acid Reactive intermediate; salt known Known only in solution and as salts Unstable, weak acid Fig. 15.2.2 (c) Stable, strong acid Fig. 15.2.2 (d) Acid unknown; Na3 NO4 and K3 NO4 have Tetrahedral been prepared NO3− 4 , Fig. 15.2.3(f)

Oxo-acids and oxo-ions of nitrogen

The oxo-acids of nitrogen known either as the free acids or in the form of their salts are listed in Tables 15.2.3 and 15.2.4. The structures of these species are shown in Figs. 15.2.2 and 15.2.3. (1) Hyponitrous acid, H2 N2 O2 Spectroscopic data indicate that hyponitrous acid, HON=NOH, has the planar trans configuration. Its structural isomer nitramide, H2 N–NO2 , is a weak acid. The structure of nitramide is shown in Fig. 15.2.2(a); in this molecule, the angle between the NNO2 plane and the H2 N plane is 52◦ . Both trans and cis forms of the hyponitrite ion, (ONNO)2− , are known. The trans isomer, as illustrated in Fig. 15.2.3(a), is the stable form with considerable π bonding over the molecular skeleton; in the cis isomer, the N=N and N–O bond lengths are 120 and 140 pm, respectively. (2) Nitroxyl, HNO This is a transient species whose structure is shown in Fig. 15.2.2(b). The existence of the NO− anion has been established by single-crystal X-ray analysis of (Et4 N)5 [(NO)(V12 O32 )], in which the NO− group lies inside the cage of Table 15.2.4. The nitrogen oxo-ions

Oxiation number

Formula

Name

Structure (Fig. 15.2.3)

Properties

+1

N2 O2− 2

Hyponitrite

Reducing agent

+2

N2 O2− 3

Hyponitrate

+3

NO− 2

Nitrite

trans, C2h , (a) cis, C2v (not shown) trans, Cs , (b) cis, Cs , (c) Bent,C2v , (d), bond angle 115◦

+5

NO− 3

Nitrate

Planar, D3h , (e)

Orthonitrate Nitrosonium Nitronium

Tetrahedral, Td , (f) C∞v , (g) D∞v , (h)

+5 +3 +5

NO3− 4 NO+ NO+ 2

Reducing agent Oxidizing or reducing agent Oxidizing agent Oxidizing agent Oxidizing agent Oxidizing agent

575

576

Structural Chemistry of Selected Elements (a)

(b)

O

115˚

N

143

N

100

H H

118 130˚

106.3

O

H

N

O

108.6˚

(d)

(c) H 95.4

Fig. 15.2.2.

121.2

Structures of two amides and two oxo-acids of nitrogen: (a) H2 N2 O2 , (b) HNO, (c) HNO2 , and (d) HNO3 .

102.1˚ 143.3 O N 110.7˚

H 96 117.7 O

102˚

116˚ O N 140.6

O 121 130˚ 121 O

(V12 O32 )4− . The bond length of NO− is 119.8 pm, which is longer than that of the neutral molecule NO, 115.0 pm. (3) Hyponitric acid, H2 N2 O3 Hyponitric acid has not been isolated in pure form, but its salts are known. In the hyponitrate anion N2 O2− 3 , both N atoms each bears a lone pair O

N

O

N

. The structure of the anion adopts a non-planar configuration, which can exist in both cis and trans forms, as shown in Figs. 15.2.3(b) and 15.2.3(c). O

2–

123.7

2–

2–

138.0

(a)

(b)

(c) 3–

1–

1–

139

122

124 115˚ Fig. 15.2.3.

(d)

Structure of nitrogen oxo-ions (bond lengths in pm): (a) trans-(ON=NO)2− , 2− (b) cis-N2 O2− 3 , (c) trans-N2 O3 , (d)

− 3− + NO− 2 , (e) NO3 , (f) NO4 , (g) NO , (h) + NO2 .

(e)

(f)

1+

1+

106 (g)

115 (h)

(4) Nitrous acid, HNO2 Although nitrous acid has never been isolated as a pure compound, its aqueous solution is a widely used reagent. Nitrous acid is a moderately weak acid with pKa = 3.35 at 291 K. In the gaseous state, it adopts the trans-planar structure, as shown in Fig. 15.2.2(c).

Group 15 Elements

577

The nitrite ion, NO− 2 is bent with C2v symmetry, and its structure can be represented by two simple resonance formulas: –O

.. N

O

O

.. N

O–

Many stable metal nitrites (Li+ , Na+ , K+ , Rb+ , Cs+ , Ag+ , Tl+ , Ba2+ , NH+ 4) contain the bent (O–N–O)− anion with N–O bond length in the range of 113-123 pm, and the angle 116◦ –132◦ , as shown in Fig. 15.2.3(d). (5) Nitric acid, HNO3 Nitric acid is one of the three major inorganic acids in the chemical industry. Its structural parameters in the gaseous state are shown in Fig. 15.2.2(d). The crystals of nitric acid monohydrate consist of H3 O+ and NO− 3 , which are connected by strong hydrogen bonds. In the acid salts, HNO3 molecules are bound to nitrate ions by strong hydrogen bonds. For example, the structures of [H(NO3 )2 ]− in K[H(NO3 )2 ] and [H2 (NO3 )3 ]− in (NH4 )H2 (NO3 )3 are as follows: −

−

O O

245 pm 121 pm N H O O 129 pm

O

O 122 pm

N

O 260 pm

O N 134 pm

H

O

O

O O 126 pm N 124 pm O

The nitrate ion NO− 3 has D3h symmetry, as shown in Fig. 15.2.3(e), and its bonding can be represented by the following resonance structures: O−

O

N+ O

O

−

−

O

N+ O

O

−

− O

−

N+ O

(6) Orthonitric acid, H3 NO4 Orthonitric acid is still unknown, but its salts Na3 NO4 and K3 NO4 have been characterized by X-ray crystallography. The NO3− 4 ion has regular Td symmetry, and its bonding can be represented by resonance structures: O

O N O

(7)

O O

O

N O

O O

Oxo-cations, NO+ and NO+ 2

O

N O

O O

N O

O O

The nitrosonium NO+ and nitronium NO+ 2 ions, which have been mentioned in previous sections, have C∞v and D∞h symmetry, respectively. Their structures shown in Figs. 15.2.3(g) and 15.2.3(h) can be represented by the familiar Lewis structures: N≡O+ and O=N+ = O.

H

O

N O

578

Structural Chemistry of Selected Elements 15.2.3

Nitrogen hydrides

(1) Ammonia, NH3 The most important nitrogen hydride is ammonia, which is a colorless, alkaline gas with a unique odor. Its melting point is 195 K. Its boiling point 240 K is far higher than that of PH3 (185.4 K). This is due to the strong hydrogen bonds between molecules in liquid ammonia. Liquid ammonia is an excellent solvent and a valuable medium for chemical reactions, as its high heat of vaporization (23.35 kJ mol−1 ) makes it relatively easy to handle. As its dielectric constant (ε = 22 at 239 K) and self-ionization are both lower than those of water, liquid ammonia is a poorer ionizing solvent but a better one for organic compounds. The self-ionization of ammonia is represented as − −33 2NH3 " NH+ (223 K), 4 + NH2 , K = 10

and ammonium compounds behave as Lewis acids while amides are bases. Ammonia is an important industrial chemical used principally (over 80%) as fertilizers in various forms, and is employed in the production of many other compounds such as urea, nitric acid, and explosives. (2) Hydrazine, H2 NNH2 Hydrazine is an oily, colorless liquid in which nitrogen has an oxidation number of −2. The length of the N–N bond is 145 pm, and there is a lone pair on each N atom. Its most stable conformer is the gauche form, rather than the trans or cis form. The rotational barrier through the trans or staggered position is 15.5 kJ mol−1 , and through the cis or eclipsed position is 49.7 kJ mol−1 . These numbers reflect the modest repulsion of the nonbonding electrons for a neighboring bond pair and the significantly greater repulsion of the nonbonding pairs for each other in the cis arrangement. The melting point of hydrazine is 275 K, and the boiling point is 387 K. The very high exothermicity of its combustion makes it a valuable rocket fuel. (3) Diazene, HN=NH Diazene (or diimide) is a yellow crystalline compound that is unstable above 93 K. In the molecule, each N atom uses two sp2 hybrids for σ bonding with the neighboring N and H atoms, and the lone pair occupies the remaining sp2 orbital. The molecule adopts the trans configuration:

H

.. N

H N ..

(4) Hydroxylamine, NH2 OH Anhydrous NH2 OH is a colorless, thermally unstable hygroscopic compound which is usually handled as an aqueous solution or in the form of its salts. Pure hydroxylamine melts at 305 K and has a very high dielectric constant (77.6–77.9). Aqueous solutions are less basic than either ammonia or hydrazine: NH2 OH(aq) + H2 O # NH3 OH+ + OH− , K = 6.6 × 10−9 (298 K).

Group 15 Elements

579

Hydroxylamine can exist as two configurational isomers (cis and trans) and in numerous intermediate gauche conformations. In the crystalline form, hydrogen bonding tends to favor packing in the trans conformation. The N–O bond length is 147 pm, consistent with its formulation as a single bond. Above room temperature the compound decomposes by internal oxidation–reduction reactions into a mixture of N2 , NH3 , N2 O, and H2 O. Aqueous solutions are much more stable, particularly acid solutions in which the protonated species [NH3 (OH)]+ is generally used as a reducing agent. 15.3

Structure and bonding of elemental phosphorus and Pn groups

Homonuclear aggregates of phosphorus atoms exist in many forms: discrete molecules, covalent networks in crystals, polyphosphide anions, and phosphorus fragments in molecular compounds. 15.3.1

Elemental phosphorus

(1) P4 and P2 molecules Elemental phosphorus is known in several allotropic forms. All forms melt to give the same liquid which consists of tetrahedral P4 molecules, as shown in Fig. 15.3.1(a). The same molecular entity exists in the gas phase, the P–P bond length being 221 pm. At high temperature (> 800◦ C) and low pressure P4 is in equilibrium with P2 molecules, in which the P≡P bond length is 189.5 pm. The bonding between phosphorous atoms in the P4 molecule can be described by a simple bent bond model, which is formed by the overlap of sp3 hybrids of the P atoms. Maximum overlap of each pair of sp3 orbitals does not occur along an edge of the tetrahedron. Instead, the P–P bonds are bent, as shown in Fig. 15.3.1(b). In a more elaborate model, the P4 molecule is further stabilized by the d orbitals of P atoms which also participate in the bonding. (2) White phosphorus White phosphorus (or yellow phosphorus when impure) is formed by condensation of phosphorus vapor. Composed of P4 molecules, it is a soft, waxy, translucent solid, and is soluble in many organic solvents. It oxidizes spontaneously in air, often bursting into flame. It is a strong poison and as little as 50 mg can be fatal to humans. (a)

(b) P

P P

P

Fig. 15.3.1.

(a) Structure of P4 molecule; (b) bent bonds in P4 molecule.

580

Structural Chemistry of Selected Elements At normal temperature, white phosphorus exists in the cubic α-form, which is stable from –77◦ C to its melting point (44.1◦ C). The crystal data of α-white phosphorus are a = 1.851 nm, Z = 56 (P4 ), and D = 1.83 g cm−3 , but its crystal structure is still unknown. At –77◦ C the cubic α-form transforms to a hexagonal β-form with a density of 1.88 g cm−3 . (3) Black phosphorus Black phosphorus is thermodynamically the most stable form of the element and exists in three known crystalline modifications: orthorhombic, rhombohedral, and cubic, as well as in an amorphous form. Unlike white phosphorus, the black forms are all highly polymeric, insoluble, and practically non-flammable, and have comparatively low vapor pressures. The black phosphorus varieties represent the densest and chemically the least reactive of all known forms of the element. Under high pressure, orthorhombic black phosphorus undergoes reversible transitions to produce denser rhombohedral and cubic forms. In the rhombohedral form the simple hexagonal layers are not as folded as in the orthorhombic form, and in the cubic form each atom has an octahedral environment, as shown in Figs. 15.3.2(a)–(c). (4) Violet phosphorus Violet phosphorus (Hittorf’s phosphorus) is a complex three-dimensional polymer in which each P atom has a pyramidal arrangement of three bonds linking it to neighboring P atoms to form a series of interconnected tubes, as shown in Fig. 15.3.3. These tubes lie parallel to each other, forming double layers, and in the crystal structure one layer has its tubes packed at right angles to those in adjacent layers. (a)

(b)

Fig. 15.3.2.

Structure of black phosphorus: (a) orthorhombic, (b) rhombohedral, and (c) cubic black phosphorus.

(c)

Group 15 Elements

Fig. 15.3.3.

Structure of the tube in violet phosphorus

(5) Red phosphorus Red phosphorus is a term used to describe a variety of different forms, some of which are crystalline and all are more or less red in color. They show a range of densities from 2.0 to 2.4 g cm−3 with melting points in the range of 585–610◦ C. Red phosphorus is a very insoluble species. It behaves as a high polymer that is inflammable and almost non-toxic. 15.3.2

Polyphosphide anions

Almost all metals form phosphides, and over 200 different binary compounds are now known. In addition, there are many ternary mixed-metal phosphides. These phosphides consist of metal cations and phosphide anions. In addition 5− to some simple anions (P3− , P4− 2 , P3 ), there are many polyphosphide anions that exist in the form of rings, cages, and chains, as shown in Fig. 15.3.4. In some metal phosphides, the polyphosphide anions constitute infinite chains and sheets, as shown in Fig. 15.3.5. 15.3.3

Structure of Pn groups in transition-metal complexes

Transition-metal complexes with phosphorus bonded to metal atoms have been investigated extensively. They include single P atoms encapsulated in cages of metal atoms, and various Pn groups where n = 2 to at least 12. These Pn groups can be chains, rings, or fragments which are structurally related to their valence electron numbers. Figure 15.3.6 shows some skeletal structures of the transition-metal complexes with Pn groups. Fig. 15.3.6(a) shows the coordination of a pair of P2 groups to metal centers in the dinuclear complex (Cp,, Co)2 (P2 )2 . In Figs. 15.3.6(b), (f), (j), and (n), the Pn groups P3 , P4 , P5 , and P6 form planar three-, four-, five-, and sixmembered rings, respectively. They can be considered as isoelectronic species of planar (CH)3 , (CH)4 , (CH)5 , and (CH)6 molecules. The [(P5 )2 Ti]2− anion [Fig. 15.3.6( j)] is the first entirely inorganic metallocene, the structure of which has a pair of parallel and planar P5 rings symmetrically positioned about the central Ti atom. The average P–P bond distance is 215.4 pm, being intermediate

581

582

Structural Chemistry of Selected Elements (a)

(b)

(c)

(e)

(f)

(h)

(d)

(g)

(i)

Fig. 15.3.4.

+ 3− 6− The structures of some polyphosphide anions: (a) P4− 6 in [Cp”Th(P6 )ThCp”] (Cp”=1,3-Bu2 C5 H3 ), (b) P7 in Li3 P7 , (c) P10 in Cu4 SnP10 , (d) 3− 2− 3− 3− 4− P3− 11 in Na3 P11 , (e) P11 in [Cp3 (CO)4 Fe3 ]P11 , (f) P16 in (Ph4 P)2 P16 , (g) P19 in Li3 P19 , (h) P21 in K4 P21 I, and (i) P26 .

Fig. 15.3.5.

Infinite chain and sheet structures of polyphosphide anions: (a) [P4− 6 ]n in

(a)

(d)

(b)

(e)

(c)

5− BaP3 , (b) [P− 7 ]n in RbP7 , (c) [P7 ]n in − Ag3 SnP7 , (d) [P15 ]n in KP15 , and (e)

[P4− 8 ]n in CuP2 .

between those of P–P single (221 pm) and P=P double (202 pm) bonds. The average Ti–P distance is 256 pm. The Ti–P5 (center) distance is 179.7 pm. The Pn groups in the complexes shown in Figs. 15.3.6(e), (k), and (o) are four-, five- and six-membered rings, respectively. Open chains P4 and P5 as

Group 15 Elements (a)

(b)

(c)

(d)

(f)

(g)

(h)

(i)

(k)

(o)

(s)

(i)

(p)

(i)

(e)

(i)

(m)

(q)

(u)

583

(n)

(r)

Fig. 15.3.6.

(v)

multidentate ligands are exemplified by the structures shown in Figs. 15.3.6(g), (h), (l), and (m). Metal complexes containing bi- and tricyclic Pn rings are shown in Figs. 15.3.6(d) and (p), respectively. The skeletons of metal complexes of polyphosphorus Pn ligands with n > 6 are shown in Figs. 15.3.6(q) to (v). The reaction of Cp*FeP5 with CuCl in CH2 Cl2 /CH3 CN solvent leads to the formation of [Cp*FeP5 ]12 (CuCl)10 (Cu2 Cl3 )5 {Cu(CH3 CN)2 }5 . In this large molecule, the cyclo-P5 rings of Cp*FeP5 are surrounded by six-membered P4 Cu2 rings that result from the coordination of each of the P atomic lone pairs to CuCl metal centers, which are further coordinated by P atoms of other cyclo-P5 rings. Thus five- and six-membered rings are fused in a manner reminiscent of the formation of the fullerene-C60 molecule. Figure 15.3.7 shows the structure of a hemisphere of this globular molecule. The two hemispheres are joined by [Cu2 Cl3 ]− as well as by [Cu(CH3 CN)2 ]+ units,

Structure of Pn groups bonded to metal atoms in transition-metal complexes: (a) (Cp”Co)2 (P2 )2 , (b) (Cp2 Th)2 P3 , (c) W(CO)3 (PCy3 )2 P4 , (d) RhCl(PPh3 )2 P4 , (e) [Cp*Co(CO)]2 P4 , (f) Cp*Nb(CO)2 P4 , (g) [Ni(CO)2 Cp]2 P4 , (h) (CpFe)2 P4 , (i) [(Cp*Ni)3 P]P4 , (j) [Ti(P5 )2 ][K(18-C-6)], (k) [Cp*Fe]P5 [Cp*Ir(CO)2 ], (l) [Cp*Fe]P5 [TaCp”], (m) [Cp*Fe]P5 [TaCp”]2 , (n) Cp*Mo2 P6 , (o) (Cp*Ti)2 P6 , (p) (Cp’2 Th)2 P6 , (q) [Cp,,, Co(CO)2 ]3 P8 , (r) [Cp*Ir(CO)]2 P8 [Cr(CO)5 ]3 , (s) (Cp, Rh)4 P10 , (t) [CpCr(CO)2 ]5 P10 , (u) CpPr Fe(CO)2 ]P11 [CpPr Fe(CO)]2 , and (v) [CpCo(CO)2 ]3 P12 .

584

Structural Chemistry of Selected Elements

Cu Fe

Fig. 15.3.7.

P Cl

Structure of a hemisphere of [Cp*FeP5 ]12 (CuCl)10 (Cu2 Cl3 )5 [Cu(CH3 CN)2 ]5 . The central Fe atom is omitted for clarity.

C

and this inorganic fullerene-like molecule has an inner diameter of 1.25 nm and an outer diameter of 2.13 nm, making it about three times as large as C60 . 15.3.4

Bond valence in Pn species

The bonding in Pn species can be expressed by their bond valence b, which corresponds to the number of P–P bonds. Let g be the total number of valence electrons in Pn . When a covalent bond is formed between two P atoms, each of them gains one electron in its valence shell. In order to satisfy the octet rule for Pn , 12 (8n − g) electron pairs must be involved in bonding between the P atoms. The number of these bonding electron pairs is defined as the bond valence b of the Pn species: b = 12 (8n − g). Applying this simple formula: P4 : b= 12 (4 × 8–4 × 5) = 6,

P3− 7

:

b= 12 [7 × 8–(7 × 5 + 3)]

6P–P bonds; = 9,

9P–P bonds;

1 P3− 11 : b= 2 [11 × 8–(11 × 5 + 3)] = 15,

1 P2− 16 : b= 2 [16 × 8–(16 × 5 + 2)] = 23,

15P–P bonds; 23P–P bonds.

In these Pn species, the b value is exactly equal to the bond number in the structural formula, as shown in Figs. 15.3.1, 15.3.4, and 15.3.5. But for the

Group 15 Elements

585

planar ring P6 [Fig. 15.3.6(n)], b = 12 [6 × 8 − (6 × 5)] = 9, which implies the existence of three P–P bonds and three P=P bonds, and hence aromatic behavior as in the benzene molecule. Cp*

(a)

(b)

Cp*

(c) Ni

OC

P P P

(d)

Nb

Rh

CO

Cp OC

g = 20, b = 6 (e)

g = 20, b = 6 (f) Cp*

Cp* Co

g = 20, b = 6 (g)

Co

Cp

(h)

CO

Ni

CO

Cp Rh

Cp

Cp*

g = 22, b = 5

g = 22, b = 5

Cp

CO

g = 24, b = 4

g = 28, b = 2

g = 32, b = 0

Cp

Fig. 15.3.8.

Structure of P4 group in some transition-metal complexes (large circle represents P atom and arrow → represents dative bond): (a) P4 molecule, (b) (P4 )Ni(PPh2 CH2 )3 CCH3 , (c) (P4 )Nb(CO)2 Cp∗ , (d) (P4 )Rh2 (CO)(Cp)(Cp∗ ), (e) (P4 )Co(CO)Cp∗ , (f) (P4 )[Co(CO)Cp∗ ]2 , (g) (P2 )2 Rh2 (Cp)2 , and (h) (P)4 (NiCp)4 .

(a)

(b)

Mo Cr P

As

(c)

(d)

Fig. 15.3.9.

P Ni

Sb Ni

Structure of transition-metal complexes 3− 3− of P3− 7 , As7 , and Sb7 : (a) 3− [P7 Cr(CO)3 ] , (b) [As7 Mo(CO)3 ]3− , (c) [P7 Ni(CO)]3− , and (d) [Sb7 Ni3 (CO)3 ]3− .

586

Structural Chemistry of Selected Elements The bond valence of a Pn group changes with its number of valence electrons. The P4 species is a good example, as shown in Fig. 15.3.8. In these structures, each transition metal atom also conforms to the 18-electron rule. The bonding structure of transition-metal complexes with Pn group can be classified into four types: (1) Covalent P–M σ bond: each atom donates one electron to bonding and the g value of Pn increases by one, as shown in Fig. 15.3.8(e). (2) P → M dative bond: the g value of Pn species does not change, as shown in Fig. 15.3.8(b). P (3) →M π dative bond: the g value of Pn species also does not change, as P shown in Fig. 15.3.8 (c). (4) (ηn –Pn ) → M dative bond: the Pn ring (n = 3–6) donates its delocalized π electrons to the M atom, and the g value of Pn group does not change. 3− 3− Some molecular transition-metal complexes of P3− 7 , As7 , and Sb7 have been isolated as salts of cryptated alkali metal ions. The structures of the complex anions are shown in Fig. 15.3.9. The bond valence b and bond number of these complex anions are as follows:

(a) [P7 Cr(CO)3 ]3− in [Rb·crypt]3 [P7 Cr(CO)3 ]: b = 12, eight P–P and four P–Cr bonds. (b) [As7 Mo(CO)3 ]3− in [Rb·crypt]3 [As7 Mo(CO)3 ]: b = 12, eight As–As and four As–Mo bonds. (c) [P7 Ni(CO)]3− in [Rb·crypt]3 [P7 Ni(CO)]: b = 12, eight P–P and four P–Ni bonds. (d) [Sb7 Ni3 (CO)3 ]3− in [K·crypt]3 [Sb7 Ni3 (CO)3 ]: b = 18, four Sb–Sb, five SbSbNi 3c-2e, and two SbNiNi 3c-2e bonds. 15.4

Bonding type and coordination geometry of phosphorus

15.4.1

Potential bonding types of phosphorus

To illustrate the potential diversity of structure and bonding of phosphorus, the classic Lewis representations for each possible coordination number one to six are shown in Fig. 15.4.1. Many of these bonding types have been observed in stable compounds, which are discussed in the following sections. (a)

(b) + .. P

.. P (h)

(i) .. P

(o) Fig. 15.4.1.

Potential bond types of phosphorus.

(c) – .. P ..

–

(m)

(s) –

(t) P

2–

P (n)

– .. P

+P

P

(g) + P

(l)

.. P (r)

P

(f) + P

(k) .. – P ..

(q) P

(e)

...P.

(j) .. + P

(p) P+

(d)

P (u)

P

P

Group 15 Elements Phosphines are classical Lewis bases or ligands in transition-metal complexes, but the cationic species shown in Fig. 15.4.1(i) are likely to exhibit Lewis acidity by virtue of the positive charge. Despite their electron-rich nature, an extensive coordination chemistry has been developed for Lewis acidic phosphorus. For example, the compound shown below has a coordinatively unsaturated Ga(I) ligand bonded to a phosphenium cation; it can be considered as a counter-example of the traditional coordinate bond since the metal center (Ga) behaves as a Lewis donor (ligand) and the non-metal center (P) behaves as a Lewis acceptor. Ph

P Ga

Dipp

15.4.2

N

Ph OTf = OTeF5– Dipp = (2,6-iC3H7)C6H3

OTf N Dipp

Coordination geometries of phosphorus

Phosphorus forms various compounds with all elements except Sb, Bi, and the inert gases for the binary compounds. The stereochemistry and bonding of phosphorus are very varied. Some typical coordination geometries are summarized in Table 15.4.1 and illustrated in Fig. 15.4.2. Many of these compounds will be discussed below. Table 15.4.1. Coordination geometries of phosphorus atoms in compounds

CN 1 2 3 4 5 6 7 8 9 10

Coordination geometry

Example

Linear Bent Pyramidal Planar Tetrahedral Square Square pyramidal Trigonal bipyramidal Octahedral Trigonal prismatic Monocapped trigonal prismatic Cubic Bicapped trigonal prismatic Monocapped square antiprismatic Tricapped trigonal prismatic Bicapped square antiprismatic

P≡N, F–C≡P [P(CN)2 ]− PX3 (X = H, F, Cl, Br, I) PhP{Mn(C5 H5 )(CO)2 }2 P4 O10 [P{Zr(H)Cp2 }4 ]+ Os5 (CO)15 (µ4 –POMe) PF5 PCl− 6 (µ6 –P)[Os(CO)3 ] − 6 Ta2 P Ir2 P Hf2 P [Rh9 (CO)21 P]2− Cr3 P [Rh10 (CO)22 P]3−

Structure (in Fig. 15.4.1) (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) (m) (n) (o) (p)

(1) Coordination number 1 Coordination number 1 is represented by the compounds P≡N, P≡C–H, P≡C– X (X = F, Cl), and P≡C–Ar (Ar =t Bu3 C6 H2 ). In these compounds, the P atom

587

588

Structural Chemistry of Selected Elements (a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m)

(n)

(o)

(p)

Fig. 15.4.2.

Coordination geometries of the phosphorus atom in some compounds (black circles represent P, open circles represent other atoms): (a) P≡N, (b) [P(CN)2 ]− , (c) PX3 , (d) PhP{Mn(C5 H5 )(CO)2 }2 , (e) P4 O10 , (f) [P{Zr(H)Cp2 }4 ]+ , (g) Os5 (CO)15 (µ4 –POMe), (h) PF5 , (i) [PCl6 ]− , (j) [Os(CO)3 ]6 P, (k) Ta2 P, (l) Ir2 P, (m) Hf2 P, (n) [Rh9 (CO)21 P]2− , (o) Cr3 P, and (p) [Rh10 (CO)22 P]3− .

forms a triple bond with the N or C atom. The bond length are P≡N 149 pm, P≡C 154 pm. (2) Coordination number 2 Compounds of this coordination number have three bond types: P

P

P

+

S P(CN)2–

R2N–P

NR

P+ = C N

2

Et

In P(CN)− 2 , the bond length P–C is 173 pm, C≡N is 116 pm, and bond angle C–P–C is 95◦ .

Group 15 Elements (3) Coordination number 3 In compounds of this coordination number, the pyramidal configuration is the most common type, and the planar one is much less favored. In pyramidal PX3 , the three X groups are either the same or different, X = F, Cl, Br, I, H, OR, OPh, Ph, t Bu, etc. The observed data of some PX3 compounds are listed below: PX3

PH3

PF3

PCl3

PBr3

PI3

P–X bond length (pm) X–P–X bond angle

144 94◦

157 96◦

204 100◦

222 101◦

252 102◦

Since PX3 has a lone pair at the P atom and the X groups can be varied, the molecules PX3 are important ligands. The strength of the coordinate bond X3 P→M is influenced by different X groups in three aspects: (a) σ P→M bonding The stability of the σ P→M interaction, which uses the lone pair of electrons on P atom and a vacant orbital on M atom, is influenced by different X groups in the sequence: Pt Bu3 > P(OR)3 > PR 3 ≈ PPh3 > PH3 > PF3 > P(OPh)3 . (b) π back donation The possibility of synergic π back donation from a nonbonding dπ pair of electrons on M into a vacant 3dπ orbital on P varies in the sequence: PF3 > P(OPh)3 > PH3 > P(OR)3 > PPh3 ≈ PR 3 > P t Bu3 . (c) Steric interference The stability of the P–M bonds are influenced by steric interference of the X groups, in accordance with the sequence: P t Bu3 > PPh3 > P(OPh)3 > PMe3 > P(OR)3 > PF3 > PH3 . In the PhP{Mn(C5 H5 )(CO)2 }2 molecule, the P atom is bonded to two Mn atoms and one phenyl C atom by single bonds in a planar configuration, as shown in Fig. 15.4.2(d). The bond angle Mn–P–Mn is 138◦ . (4) Coordination number 4 This very common coordination number usually leads to a tetrahedral configuration for phosphoric acid, phosphates, and many phosphorus(V) compounds. In these compounds, the P(V) atom forms one double bond and three single bonds with other atoms. Figure 15.4.2(e) shows the structure of P4 O10 , whose symmetry is Td . The length of the terminal P=O bond is 143 pm, and the bridging P–O bond is 160 pm. The bond angle O–P–O is 102◦ , and P–O–P is 123◦ . The compound P4 O10 , known as “phosphorus pentoxide,” is the most common and most important oxide of phosphorus. This compound exists in three modifications. When phosphorus burns in air and condenses rapidly from the

589

590

Structural Chemistry of Selected Elements vapor, the common hexagonal (H) form of P4 O10 is obtained. The H form is metastable and can be transformed into a metastable orthorhombic (O) form by heating for 2 h at 400◦ C, and into a stable orthorhombic (O, ) form by heating for 24 h at 450◦ C. All three modifications undergo hydrolysis in cold water to give phosphoric acid, H3 PO4 . Square-planar geometry of the P atom occurs in the compound [P{Zr(H)Cp2 }4 ][BPh4 ]. Figure 15.4.2(f) shows the structure of P{Zr(H)Cp2 }+ 4, in which the Zr–P–Zr angles are very close to 90◦ , and the bridging hydrogens and the Zr atoms form a nearly planar eight-membered ring that encircles the central P atom. (5) Coordination number 5 Figure 15.4.2(g) shows the structure of Os5 (CO)15 (µ4 -POMe), in which five Os atoms constitute a square-pyramidal cluster. Each Os atom is coordinated by three CO ligands, and only the four basal Os atoms are bonded to the apical P atom. Various structures have been found for phosphorus pentahalides: (a) The molecular structure of PF5 is trigonal bipyramidal, as shown in Fig. 15.4.2(h). The axial P–F bond length is 158 pm, which is longer than the equatorial P–F bond length of 153 pm. (b) In the gaseous phase, PCl5 is trigonal bipyramidal with axial P–Clax bond length 214 pm and equatorial P–Cleq bond length 202 pm. In the crystalline phase, PCl5 consists of a packing of tetrahedral [PCl4 ]+ and octahedral [PCl6 ]− ions; in the latter anion shown in Fig. 15.4.2(i), the P–Cl bond length is 208 pm. (c) In the crystalline phase, PBr5 consist of a packing of [PBr4 ]+ and Br− . Owing to steric overcrowding, [PBr6 ]− cannot be formed by grouping six bulky Br atoms surrounding a relatively small P atom. (d) There is as yet no evidence for the existence of PI5 . (6) Coordination number ≥ 6 In each of the structures shown in Figs. 15.4.2(j)–(p), the transition-metal atoms form a polyhedron around the P atom, which donates five valence electrons to stabilize the metal cluster.

15.5

Structure and bonding in phosphorus–nitrogen and phosphorus–carbon compounds

15.5.1

Types of P–N bonds

When phosphorus and nitrogen atoms are directly bonded, they form one of the most intriguing and chemically diverse linkages in inorganic chemistry. A convenient classification of phosphorus–nitrogen compounds can be made on the basis of formal bonding. Azaphosphorus compounds containing the P–N group are known as phosphazanes, those containing the P=N group are

Group 15 Elements Table 15.5.1. The common types of phosphorus-nitrogen bonds∗

Phosphazanes P

N

(sp2) σ2, λ2

P

N

(sp3) σ3, λ3

+ P

N

(sp3) σ4, λ4

P

N

(sp3) σ4, λ5

P

N

(sp3d) σ5, λ5

N

(sp3d) σ5, λ5

N

(sp3d2) σ6, λ6

PIII

P

V

Phosphazenes

P

P

+

P

N

(sp2) σ2, λ3

P

N

(sp3) σ4, λ5

P

N

(sp3) σ4, λ5

P

N

(sp3) σ4, λ5

P

N

(sp2) σ3, λ5

N

N

N

Phosphazenes P

P

N σ1, λ3

2 3 5 N (sp ) σ , λ

∗ The hybridization of the P atom is enclosed in parentheses. The symbols σ and λ represent the coordination number and bonding number of P atoms.

phosphazenes, and those with the P≡N group are phosphazynes. The common types of phosphorus–nitrogen bonds of these three classes of compounds are displayed in Table 15.5.1. Phosphazynes are rare. The bond length of the diatomic molecule P≡N is 149 pm. The first stable compound containing the P≡N group is [P≡N– R]+ [AlCl4 ]− , [R = C6 H2 (2,4,6-t Bu3 )], in which the length of the P≡N bond is 147.5 pm.

15.5.2

Phosphazanes

Some examples of phosphazanes are described below according to the types of P–N bonds. (1)

..P N +

In this bonding type, the P atom uses its sp2 hybrid orbitals, one of which accommodates a lone pair. A bent molecular structure of this type

591

592

Structural Chemistry of Selected Elements is found for (t Pr2 N)2 P+ : .. R2N

+..

P

.. NR2

+

R2N

.. P

.. NR2

.. R2N

.. P

+

NR2

The bond length of P–N is 161.2 pm, shorter than the standard P–N singlebond distance of 177 pm observed in H3 N–PO3 , which does not have a lone pair on the N atom. The bond angle N–P–N is 115◦ , smaller than idealized 120◦ , due to the repulsion of the lone pairs. (2)

.. P N

The configuration of most R2 P–NR2 compounds is represented by F2 P–NMe2 , which features a short P–N distance (162.8 pm) and trigonal planar arrangement (sp2 hybridization) at the N atom. The plane defined by the C2 N unit bisects the F–P–F angle. This configuration minimizes steric repulsion between the substituents on P and N and also orients the lone pairs on the P and N atoms at a dihedral angle of about 90◦ , as shown in Fig. 15.5.1(a). The geometry of the molecule and the short P–N distance indicate that there is π bonding between the P and N atoms. In the molecule, the z axis is perpendicular to the PNC2 plane and the x axis lies parallel to the P–N bond. The pz (N) orbital with a lone pair and the empty dxz (P) orbital overlap to form a π bond, as shown in Fig. 15.5.1(b). The structure of F2 PNH2 resembles that of F2 PNMe2 with a P–NH2 bond distance of 166 pm. (3)

+

P N

Many compounds contain formally a single-bonded P–N group, such as the cation [PCl2 (NMe2 )2 ]+ in crystalline [PCl2 (NMe2 )2 ](SbCl6 ), the cation [P(NH2 )4 ]+ , and the anion [P(NR)4 ]3− . The bond length of P–N in [P(NH2 )4 ]+ is 160 pm, and that in [P(NR)4 ]3− is 164.5 pm. (4)

P N

An important group of compounds such as (Me2 N)2 POCl, (Me2 N)POCl2 , and (R2 N)3 PO possess this bonding type. For example, (Me2 N)3 PO is a colorless (a)

(b) y

90˚

P 162.8 N 161.0 F

116˚

z x

x

124˚ Me

Fig. 15.5.1.

(a) Molecular structure of F2 P–NMe2 , (b) overlap between the dxz orbital of the P atom and the pz orbital of the N atom.

Group 15 Elements mobile liquid which is miscible with water in all proportions. It forms an adduct with HCCl3 , dissolves ionic compounds, and can dissolve alkali metals to give blue paramagnetic solutions which are strong reducing agents.

(5)

P N

The compound F4 P–NEt2 has this bonding type, in which the P atom uses sp3 d hybrid orbitals.

(6)

+ P

N

The phosphatranes that have this bonding type are analogs of silatranes. The cage molecule shown on the right is a trigonal bipyramidal five-coordinated phosphazane with a rather long P–N bond.

(7)

P

+

N

The adduct F5 P←NH3 is an octahedral six-coordinated phosphanane, in which the P–N bond length is 184.2 pm. In another example, Cl5P

N

N, the P–N

bond length is 202.1 pm, which is longer than the former. This difference is due to the high electronegativity of F, which renders the F5 P group a better acceptor as compared to Cl5 P.

15.5.3

Phosphazenes

Phosphazenes, formerly known as phosphonitrilic compounds, are characterized by the presence of the group P=N. Known compounds, particularly those containing the P N group, are very numerous and they have important potential applications.

(1) Bonding types of phosphazenes (a) Containing –P=N– bonding type In this bonding type, the P atom uses sp2 hybrid orbitals, one of which contains the lone-pair electrons. This type of phosphazene compounds exists in a bent configuration. For example, the structure of (SiMe3 )2 NPN(SiMe3 ) is shown below: 167.4 pm

(Me3Si)2N

108o

P

154.5 pm

N

SiMe3

593

594

Structural Chemistry of Selected Elements (b) Containing P N

bonding type

The compound (Me3 Si)2 N–P(NSiMe3 )2 belongs to this type, as shown below: Me3SiN 150.3 pm

164.6 pm

Me3SiN

(c) Containing P N

N(SiMe3)2

P

113o

bonding type

The simplest compound of this type is iminophosphorane, H3 P=NH, whose derivatives are very numerous, including R3 P=NR, , Cl3 P=NR, (RO)3 P=NR, , and Ph3 P=NR. In these compounds the P atom uses its sp3 hybrid orbitals to form four σ bonds, and is also strengthened by dπ−pπ overlap with N and other atoms. (2) Structure and bonding of cyclic phosphazenes The main products of refluxing a mixture of PCl5 and NH4 Cl using tetrachloroethane as solvent are the cyclic trimer (PNCl2 )3 and tetramer (PNCl2 )4 , which are stable white crystalline compounds that can be isolated and purified by recrystallization from nonpolar solvents. The trimer (PNCl2 )3 has a planar six-membered ring structure of D3h symmetry with the six Cl atoms disposed symmetrically above and below the plane of the ring. The P–N bonds within the ring are of the same length, 158 pm, and the interior angles are all close to 120◦ . The Cl–P–Cl planes are perpendicular to the plane of the central ring, and the Cl–P–Cl angle is 120◦ . Figure 15.5.2 shows the structures of (PNCl2 )3 and chair-like (PNCl2 )4 . The shortness and equality of the P–N bond lengths in (PNCl2 )3 arise from electron delocalization involving the d orbitals of the P atoms and the p orbitals of the N atoms. In such a system, the σ bonds formed from phosphorus sp3 orbitals overlapping with the nitrogen sp2 orbitals are enhanced by π bonding between the nitrogen pz orbitals and the phosphorus d orbitals. In (PNCl2 )3 , the π bonding occurs over the entire ring. Firstly, dπ−pπ overlap occurs between the nitrogen pz orbital (z axis perpendicular to the ring plane) and the dxz orbital of phosphorus. Figure 15.5.3(a) shows the orientation of one dxz orbital of the P atom and two pz orbitals of neighbor N atoms. Figure 15.5.3(b) shows a projection of the overlap of dxz with the pz orbitals. Secondly, “in-plane” electron delocalization probably arises from overlap of the (a)

Fig. 15.5.2.

Structure of (a) (PNCl2 )3 and (b) (PNCl2 )4 (circles of decreasing sizes represent Cl, P, and N atoms, respectively).

(b)

Group 15 Elements (a)

z

(b)

595

y dxz

dxz pz

x pz

(c)

(d)

y

dxz

Fig. 15.5.3.

dx2-y 2

dπ–pπ Bonding in the ring of (PNCl2 )3 : (a) orientation of dxz of P atom and pz of N atom; (b) overlap of dxz and pz ; (c) overlap of dx2 −y2 of P atom and lone

pz x

pair (sp2 ) of N atom; (d) possible mismatch of the dxz orbital of P atom and pz orbital of the N atom.

--

--

lone-pair orbitals on nitrogen with the dx2 −y2 orbitals on phosphorus, forming additional π , bonds in the plane of the ring. Fig. 15.5.3(c) shows the dx2 −y2 of P overlapping with the lone-pair (sp2 ) orbitals of two adjacent N atoms. Thirdly, the dz2 orbitals of P atoms overlap with the p orbitals of the exocyclic Cl atoms. Fig. 15.5.3(d) shows that electron delocalization around the ring is hindered by a mismatch of orbital symmetry. A simplified description of the bonding in this molecule based on the group-theoretic method is given in Chapter 7. The geometric disposition of the d orbitals in dπ –pπ systems allows puckering and accounts for the variety of ring conformations found among larger cyclic phosphazene compounds, such as (PNCl2 )4 . Of the five binary phosphorus–nitrogen molecules described in the literature, namely P4 N4 , P(N3 )3 , P(N3 )5 , the anion in the ionic compound (N5 )+ [P(N3 )6 ]− , and the phosphazene derivative [PN(N3 )2 ]3 , only the last has been fully structurally characterized. These compounds are difficult to isolate and handle owing to their highly endothermic character and extremely low energy barriers, which often lead to uncontrollable explosive decomposition. Single-crystal X-ray analysis of [PN(N3 )2 ]3 conducted in 2006 showed that it is a structural analog of [PNCl2 ]3 , with three azide groups oriented nearly parallel to the phosphazene ring and the other three nearly perpendicular to the ring. A hybrid borazine-phosphazine ring system + Cl has been found in [ClBNMePCl2 NPCl2 NMe](GaCl4 ); an X-ray study revealed that the 6π aromatic cation (structural formula shown on the right) is virtually planar with B–N bond lengths of 143.6(9) and 142.2(10) pm, which are close to those found in borazines (143 pm).

Me

B N

Cl Cl

Me N

P

P N

Cl Cl

596

Structural Chemistry of Selected Elements All phosphazenes, whether cyclic or chain-like, contain the formally unsaturated group P=N with four-coordinate P and two-coordinate N atoms. Based on available experimental data, the following generalizations may be made in regard to their structure and properties: (a) The rings and chains are very stable. (b) The skeletal interatomic distances are equal within the ring or along the chain, unless there is different substitution at various P atoms. (c) The P–N distances are shorter than expected for a covalent single bond (∼177 pm) and are usually in the range 158±2 pm. (d) The N–P–N angles are usually in the range 120 ± 2◦ ; but the P–N–P angles in various compounds span the range 120◦ –148◦ . (e) Skeletal N atoms are weakly basic and can coordinate to metals or be protonated, especially when the P atoms carry electron-releasing groups. (f) Unlike many aromatic systems, the phosphazene skeleton is difficult to reduce electrochemically. (g) Spectral effects associated with organic π systems are not exhibited. 15.5.4

Bonding types in phosphorus–carbon compounds

Phosphorus and carbon are diagonal relatives in the Periodic Table. The diagonal analogy stresses the electronegativity of the element (C 2.5 vs P 2.2) which governs its ability to release or accept electrons. This property controls the reactivity of any species containing the element. This section covers the types of phosphorus–carbon bonds and the structures of representative species. (1)

Phosphinidenes and phosphinidene complexes,

C

P

Phosphinidenes (recommended IUPAC name: phosphanylidenes) are unstable species and analogous to the carbenes. The parent compound H–P is a sixelectron species that is still unknown, but its organic derivatives can give rise to seven different types of complexes, as listed in Table 15.5.2. (2) Phosphaalkenes, R 1 R 2 C=PR 3 Phosphaalkenes are tervalent phosphorus derivatives with a double bond between carbon and phosphorus. The observed P=C bond lengths range from 161 to 171 pm (average 167 pm), appreciably shorter than the single P–C bond length of 185 pm. Phosphaalkenes may coordinate to transition-metal fragments in various ways: (a) η1 mode via the lone pair on P atom. An example is Mes

Ph C Ph

P

P Cr(CO)5

C 167.9 pm

Group 15 Elements

597

Table 15.5.2. Types of phosphinidene complexes

Types

Structure and properties

..

P

Two-electron complexes

M

R

η1 -bent, electrophilic

..

M

P

η1 -bent, nucleophilic∗

R

..

P

R

Four-electron complexes

M

µ2 -pyramidal

M

η1 -linear†

M

R

P

R

P

M µ2 -planar

M R M

P M

µ3 -tetrahedral

M

M R

P M

M

µ4 -bipyramidal

M

∗

In the complex Mes–P=Mo(Cp)2 , P=Mo 237.0 pm, Mo –P –C 115.8◦ . In the complex Mes–P≡WCl2 (CO)(PMePh2 ), P≡W 216.9 pm, C–P–W 168.2◦ . †

(b) η2 mode via the π bond electrons. An example is Cp*

Tms C Cp*

P Ni(PEt3)2

In η2 complexes the P–C bond length is longer than that in η1 complexes or the free ligands. (c) η1 , η2 mode via both the lone pair and π bond electrons. An example is 154.0

Mes* H2C

P

P

C

147.3 153.9

173.7 pm

154.8 P

Fe(CO)4 Fe(CO)4

(3) Phosphaalkynes, RC≡P Phosphaalkynes are compounds of tervalent phosphorus which contain a P≡C triple bond. Figure 15.5.4 shows the structure of t Bu–C≡P, whose P≡C bond

Fig. 15.5.4. Structure of t Bu–C≡P (bond lengths in

pm).

598

Structural Chemistry of Selected Elements Table 15.5.3. Coordination modes of phosphaalkynes

Coordination mode

η1

Example and structure

R

C

R

C

[tBu–C≡P–Fe(H)(dppe)2][BPh4] C≡P 151.2 pm

M

P

t

P

Bu

C

P

η2

M R

η1, η2

C

Pt(PR3) M

P

t

Bu

C

Cr(CO)5

P

Pt(Ph2PCH2CH2PPh2)

M M t

R

4e

C

P

BuCP[Fe2(CO)5(PPh2CH2PPh2)] [Fig. 15.5.5(a)]

M

M t

6e

R

C

M

P

BuCP[W(CO)5][Co2(CO)6] [Fig. 15.5.5(b)]

M

is very short (154.8 pm), and the electronic ionization energies [I1 (π MO) = 9.61 eV, I2 (P lone pair) = 11.44 eV] are low, suggesting that it may have a chemistry closely related to that of the alkynes. Phosphaalkynes have a rich coordination chemistry, in which both the triple bond and the lone pair of the P atom can participate. Table 15.5.3 lists the coordination modes of phosphaalkynes, and two structures are shown in Fig. 15.5.5. (a)

(b) W(CO)3 P

Fig. 15.5.5.

Structure of (a) t Bu-CP[Fe2 (CO)5 (PPh2 CH2 PPh2 )] and (b) t Bu-CP[W(CO)5 ][Co2 (CO)6 ].

Fe(CO)2

PPh2

Co(CO)3

Some oligomers of the phosphaalkynes t BuCP have been characterized. The phosphaalkyne cyclotetramer exists in several isomeric forms, whose structures are shown in Fig. 15.5.6(a) to Fig. 15.5.6(e). In cubane-like P4 C4 t Bu4 , the P–C bond lengths are all identical (188 pm), and are typical for single bonds. The angle at P is reduced from the idealized 90◦ to 85.6◦ , while that at C is widened to 94.4◦ . The phosphaalkyne pentamer P5 C5 t Bu5 has the cage structure shown in Fig. 15.5.6(f), which can be derived from the tetramer by replacing one corner C atom of the “cube” by a C2 P triangular fragment.

Group 15 Elements (a)

(b)

(c)

(e)

599

(d)

(f)

(g)

Fig. 15.5.6.

Structure of oligomers of phosphaalkyne: (a)–(e) cyclotetramer, (f) pentamer, (g) hexamer.

The phosphaalkyne hexamer P6 C6 t Bu6 consists of a lantern-like cage constructed from the linkage of a chair-like P4 C2 ring with a pair of C2 P rings above and below it, as shown in Fig. 15.5.6(g). (a)

(b) Ph

Ph P4

Ph Ph

H Ru

P3 Ph

P5

Ph Ph

Ph Ph

P2

P1

Ph

Ph

SiPh3

P4 P3

Ph C

H Ru

C

P5 P2

Ph Ph Ph

P1

(4) Cyaphide P≡C− The quest for cyaphide, the phosphorus homolog of cyanide, as a ligand in a stable metal complex came to a satisfactory conclusion in 2006. The pair of related complexes [RuH(dppe)2 (Ph3 SiC≡P)]OTf and [RuH(dppe)2 (C≡P)] were obtained via a new synthetic route and structurally characterized by Xray crystallography. Their molecular geometries are displayed in Fig. 15.5.7. As expected, the Si–C≡P and P≡C− ligands are P- and C-coordinated to the Ru(II) center, respectively. The long C≡P bond in the cyaphide complex likely arises from back donation from Ru to the π ∗ orbitals of the ligand.

Fig. 15.5.7.

Molecular structures and bond lengths (pm) of (a) [RuH(dppe)2 (Ph3 SiC≡P)]+ , C≡P1 153.0(3), Ru–P1 224.85(8), Ru–P2 238.11(7), Ru–P3 237.21(7), Ru–P4 235.59(7), Ru–P5 236.94(7); (b) [RuH(dppe)2 (C≡P)], C≡P1 157.3(2), Ru–C 205.7(2), Ru–P2 233.42(5), Ru–P3 233.15(5), Ru–P4 232.22(5), Ru–P5 233.96(4).

600

Structural Chemistry of Selected Elements Table 15.5.4. Coordination modes of diphosphenes

Coordination mode

Example and structure

Mo2P2 in a butterfly configuration

Fe2P2 in a tetrahedral configuration

15.5.5

π-Coordination complexes of phosphorus–carbon compounds

(1) Diphosphenes (R–P==P–R) Diphosphenes contain the –P==P– group, the majority of which adopt a transconfiguration. For example, the stable compound

Ar

Ar .. P P..

(Ar = 2, 4, 6- t Bu3 C6 H2 )

exhibits the trans form with a P==P bond length of 203.4 pm. Various coordination modes of diphosphenes toward transition metals involve σ and π interaction with the metal center, as listed in Table 15.5.4.

Group 15 Elements (2) η3 -Phosphaallyl and η3 -phosphirenes The phosphaallyl anions ( the group (

P

C

) and the phosphirenes which contain

P

) are η3 −ligands that can form complexes with transition

P

metals. Some examples are shown below: t

H

H

H C

Mes*O P

P

H Co(CO)3

P

Bu

(OC)3Cr

t

Bu

Ni

C CH2 H MoCp(CO)2

P P

P t

Bu

(3) η4 -Phosphadienes and diphosphacyclobutadienes Phosphadienes,

P

C

C

C

or

C

P

C

, are η4 -ligands

C

that can form complexes with transition metals, for example:

OMe C CMe

(CO)5W P Ph

HC W(CO)4

H C CH3

Ph

C H

W(CO)5

P HC

CHMe2

Fe(CO)3

Many metal complexes containing the 1,2 or 1,3-diphosphacyclobutadiene ring have been characterized, and Fig. 15.5.8 shows the structures of some examples. Interestingly, it has proved impossible to displace the η4 -ligated (P2 C2 t Bu2 ) rings from any of the above complexes, in contrast with the behavior of the analogous η4 -ligated cyclobutadiene ring complexes. This may be attributed to the significantly stronger π interaction between the metal and the phosphoruscontaining ring system. (4) η5 -Phospholyl complexes The phospholyl unit, which contains one to five P atoms, is an analog of the cyclopentadienyl ligand. Figures 15.5.9(a) to 15.5.9(f) show some phosphametallocenes, including sandwich, half-sandwich, and tilted structures. Figures 15.5.9(g) to 15.5.9(j) show some complex phosphametallocenes, in which only essential parts of the structure are displayed. Figure 15.5.9(k) shows the supramolecular structure of [Sm(η5 -PC4 Me4 )2 (η1 -PC4 Me4 )K(η6 C6 H5 Me)]Cl.

601

602

Structural Chemistry of Selected Elements (a)

(b)

(c)

(e)

(f)

P

(d)

Fig. 15.5.8.

Structure of diphosphacyclobutadiene complexes: (a) Fe(CO)3 [η4 -P2 C2 t Bu2 ], (b) Ni[η4 -P2 C2 t Bu2 ]2 , (c) Mo[η4 -P2 C2 t Bu2 ]3 , (d) Ti(η4 -P2 C2 t Bu2 )(η8 -COT), (e) Co(η4 -P2 C2 t Bu2 )(η5 -P2 C3 t Bu3 ), and (f) Rh(η4 -P2 C2 t Bu2 )(η5 -C2 B9 H11 ).

(5) η6 -Phosphinine complexes The phosphinine rings (PC5 R5 , P2 C4 R4 ,. . . P6 ) are analogs of benzene and form sandwich structures with the transition metals. In η6 -phosphinine complexes, the phosphinine rings are all planar.

15.6

Structural chemistry of As, Sb, and Bi

15.6.1

Stereochemistry of As, Sb, and Bi

The series As, Sb, and Bi show a gradation of properties from non-metallic to metallic, but the discrete molecules and ions of these elements exhibit similar stereochemistry, as listed in Table 15.6.1 and shown in Fig. 15.6.1. The presence of a lone pair (denoted by E in the table) in these atoms implies MIII ; otherwise it is MV . Many compounds of the MX3 E type have been prepared, and all 12 trihalides of As, Sb, and Bi are well known and available commercially. In either the gaseous or solid state, the lone pair causes the bond angles to be less than the ideal tetrahedral angle in every case. For example, SbCl3 in the gas phase has bond length 233 pm and bond angle 97.1◦ , and in the crystal it has three short Sb–Cl 236 pm and three long Sb· · · Cl ≥ 350 pm, and the bond angle Cl–Sb–Cl − is 95◦ . The cations of MX+ 4 are all tetrahedral. The anion SbF4 is known in the monomeric form and has the MX4 E type disphenoidal geometry. In the dimer Sb2 F− 7 both Sb atoms have a disphenoidal geometry with the bridging fluorine in one axial position.

Group 15 Elements (a)

(b)

(c)

(d)

603

(e)

(f)

M M

M

M

(g)

(h)

Sn

M

(i)

P

(j) Rh Cr

Mo

Mo

Cr

Fe

(k)

K

Cl Sm

P

Fig. 15.5.9.

Structure of phospholyl π complexes: (a)–(e) sandwich-type phosphametallocenes, (f) Sn[η5 -PC4 (TMS)2 Cp2 ]2 , (g) (η3 -C9 H7 )Mo(CO)2 (η5 -P2 C3 t Bu3 ), (h) (η3 -P2 C3 t Bu3 )Mo(CO)2 (η5 -Cp∗ ), (i) [(η5 -Cp∗ )(CO)]Rh[η5 -P3 C2 t Bu2 ]Fe(η5 -Cp), (j) (η5 -Cp∗ )Cr(η5 -P5 )Cr(η5 -Cp∗ ), (k) [Sm(η5 -PC4 Me4 )2 (η1 -PC4 Me4 )K(η6 -C6 H5 Me)]Cl. Table 15.6.1. Stereochemistry of As, Sb, and Bi

Total number of electron pairs

General formula*

∗M

Geometry

4

MX3 E

4

MX4

Trigonal pyramidal

5

MX4 E

5 5

MX5 MX5

6

MX5 E

6

MX6

Octahedral

7

MX6 E

Octahedral

Tetrahedral

Example (refer to Fig. 15.6.1) AsCl3 , SbCl3 , BiCl3 (a)

+ AsCl+ 4 , SbCl4 (b)

Disphenoidal Trigonal bipyramidal

SbF− 4 (c) AsF5 , SbCl5 , BiF5 (d)

Square pyramidal

Sb(C6 H5 )5 , Bi(C6 H5 )5 (e)

Square pyramidal

SbCl2− 5 (f)

= As, Sb, or Bi, X = ligand atom or group, E = lone pair.

SbBr− 6 (g)

3− SbBr3− 6 , BiBr6 (g)

604

Structural Chemistry of Selected Elements (a)

(e)

(b)

(c)

(f)

(d)

(g)

Fig. 15.6.1.

Stereochemistry of As, Sb, and Bi: − (a) AsCl3 , (b) AsCl+ 4 , (c) SbF4 , (d)

SbCl5 , (e) Bi(C6 H5 )5 , (f) SbCl2− 5 , and

3− (g) SbBr3− 6 and BiBr6 .

Compounds of the MX5 type exhibit two geometries, trigonal bipyramidal (more common) and square pyramidal. In the trigonal bipyramidal molecules, the axial bonds are longer than the equatorial bonds. If there are different ligands, the more electronegative ones usually occupy the axial positions. The compounds Bi(C6 H5 )5 and Sb(C6 H5 )5 have a square-pyramidal shape, as shown in Fig. 15.6.1(e), for which the bond lengths and bond angles are as follows: Bi(C6 H5 )5 : Bi–Cax 222.1 pm Bi–Cba 233.6 pm Cax –Bi–Cba 101.6◦ Sb(C6 H5 )5 : Sb–Cax 211.5 pm Sb–Cba 221.6 pm Cax –Sb–Cba 105.4◦ 2− The molecules of MX5 E type, such as SbF2− 5 , BiCl5 , and some oligolymeric 4− 2− anions (SbF4 )4 and (BiCl4 )2 , have square-pyramidal geometry at each M atom. In these cases, the four ligands in the base of the square pyramid lie in a plane slightly above the central M atom, and the bond angles are all less than 90◦ caused by the greater lone-pair repulsions. − − The anions of the type MX6 , such as SbF− 6 , SbBr6 , and Sb(OH)6 , have the expected octahedral geometry. The anions of the type MX6 E, such as SbBr3− 6 and BiBr3− , frequently also have a regular octahedral structure. The undistorted 6 nature of the SbBr3− 6 octahedral suggests that the lonepair is predominantly 5s2 , but in a sense it is still stereochemically active since the Sb–Br distance in V − SbIII Br3− 6 is 279.5 pm, which is longer than the distance 256.4 pm in Sb Br6 . The bismuthonium ylide 4,4-dimethyl-2,6-dioxo-1-triphenylbismuthoniocyclohexane exhibits a distorted tetrahedral geometry with a Bi–Cylide bond length of 215.6 pm, Bi–CPh bond lengths in the range 221–2 pm, and a weak Bi· · ·O interaction of 301.9 pm with one of the carbonyl oxygen atoms (the other Bi· · ·O separation is 335.2 pm). The X-ray data are consistent with the expectation that the negative charge resides mainly on a deprotonated enolic oxygen atom rather than on the ylidic carbon atom, whose 2p orbital does not overlap effectively with the 6d orbital of bismuth. Accordingly, formula I

Group 15 Elements

605

is a faithful representation of the structure in preference to II, III, and IV, as displayed below: I

II

_ O

O + Bi Ph Ph

_ O

O Ph Ph

Ph

III

_ O

O +

+ Bi

Ph

Ph Ph

Bi Ph

IV

_

O Ph Ph

Bi

O

Ph

E R

W N

R = SiMe3 R

N N

N

15.6.2

W P W As W Sb

O

+

From 1995 onward, studies have led to the synthesis and structural characterization of stable tungsten complexes with a heavier Group 15 element functioning as a triple-bonded terminal ligand. In the series of complexes [(CH2 CH2 NSiMe3 )3 N]W≡E (E = P, As, Sb), the tungsten atom exhibits a distorted trigonal bipyramidal coordination geometry with three equatorial N atoms and one N atom and the E atom occupying the axial positions. The molecular structure and W≡E bond distances are shown below:

R

O

216.2(4) pm 229.0(1) pm 252.6(2) pm

Metal–metal bonds and clusters

Many compounds containing M–M bonds or stable rings and clusters of Group 15 elements are known. Figures 15.6.2(a) to 15.6.2(c) show the structures of some organometallic compounds of As, Sb, and Bi, which contain M–M bonds, and Figs. 15.6.2(d) to 15.6.2(e) show the structures of naked cluster cations Bim+ n , which are the components of some complex salts of bismuth. The structure of As6 (C6 H5 )6 illustrates the typical trigonal pyramidal environment of the As atom; the As–As bond length is 246 pm, in which the As6 ring adopts a chair conformation. In Sb4 (η1 -C5 Me4 )4 , Sb4 forms a twisted ring, with Sb–Sb 284 pm, and all Sb–Sb–Sb bond angles are acute. Tetrameric bis(trimethylsilyl)methylbismuthine [(Me3 Si)2 CHBi]4 contains a folded four-membered metallacycle with fold angles of 112.6◦ and 112.9◦ , Bi–Bi bond lengths in the range 297.0–304.4 pm, and Bi–Bi–Bi angles in the range 79.0–79.9◦ . The discrete molecules As2 Ph4 , Sb2 Ph4 , and Bi2 Ph4 all adopt the staggered conformation, and the bond lengths are As–As 246 pm, Sb–Sb 286 pm, and Bi–Bi 299 pm. Dibismuthenes of the general formula LBi=BiL can be synthesized when L is a bulky aryl ligand. The LBi=BiL molecule is centrosymmetric and therefore exists in the trans configuration. For L = 2,4, 6-tris[bis(trimethylsilyl)methyl]phenyl, X-ray analysis of the dibismuthene

Ph Ph

Bi Ph

606

Structural Chemistry of Selected Elements (a)

(b)

(c)

Bi Sb

As

(d)

(e)

(f)

Fig. 15.6.2.

Structures of (a) As6 (C6 H5 )6 , (b) Sb4 (η1 -C5 Me4 )4 , (c) Bi2 (C6 H5 )4 , 2+ 5+ (d) Bi3+ 5 , (e) Bi8 , and (f) Bi9 . In (a)–(c) the phenyl ligands are represented by C atoms bonded to the metal skeleton.

yielded a Bi=Bi double-bond length of 282.1 pm and a Bi==Bi–C angle of 100.5◦ . 2+ 5+ The structures of cationic bismuth clusters Bi3+ 5 ,Bi8 , and Bi9 are listed in Table 15.6.2. Table 15.6.2. Cationic bismuth clusters

Cation

Crystal

Structure

Symmetry

Bi3+ 5

Bi5 (AlCl4 )3

Trigonal bipyramidal

D3h

Bi8 (AlCl4 )2

Square antiprism

D4h

Bi24 Cl28 , or 2− 2− (Bi5+ 9 )2 (BiCl5 )4 (Bi2 Cl8 )

Tricapped trigonal prism

C3h (∼D3h )

Bi2+ 8 Bi5+ 9

Metalloid and intermetalloid clusters of Group 13 and 14 elements have been described in the two preceding chapters. For Group 15 elements, the ligandfree intermetalloid clusters [As@Ni12 @As20 ]3− and [Zn@Zn8 Bi4 @Bi7 ]5− are known. In [As@Ni12 @As20 ]3− , a central As atom is located inside a Ni12 icosahedron, which is in turn enclosed by a As20 pentagonal dodecahedron, as shown in Fig. 15.6.3(a). The first example of an intermetalloid cluster that almagamates 11 Bi and 9 Zn atoms has been found in the complex [K(2.2.2-crypt)]5 [Zn9 Bi11 ]· 2en·toluene (2.2.2-crypt = 4,7,13,16,21,24-hexaoxa-1,10-diazabicyclo[8.8.8] hexacosane). The naked [Zn@Zn8 Bi4 @Bi7 ]5− cluster consists of a central Zn atom trapped inside a distorted icosahedron whose vertices are 8 Zn atoms and 4 Bi atoms, with 7 of the 20 triangular faces each capped by a Bi atom, as shown in Fig. 15.6.3(b). A simplified model may be used to rationalize the bonding in the heteroatomic species [Zn@Zn8 Bi4 @Bi7 ]5− . According to the electron counting theory proposed by Wade, the formation of a closo deltahedra of 12 vertices is stabilized by 13 skeletal electron pairs. The total of 26 electrons required for skeletal bonding may be considered to be provided as follows: 2 from the interstitial Zn atom, (8 × 0 + 4 × 3 = 12) from the Zn8 Bi4 icosahedral unit (each vertex atom carries an exo lone pair or bond pair), 7 from the capping Bi atoms, and 5 from

Group 15 Elements (a)

(b)

Fig. 15.6.3.

(a) Structure of the [As@Ni12 @As20 ]3− cluster; the solid and open circles represent Ni and As atoms, respectively. (b) Structure of the [Zn@Zn8 Bi4 @Bi7 ]5− cluster; the shaded and open circles represent Zn and Bi atoms, respectively. Interatomic distrances: Zncent –Znico 283.2(2)–359.4(3), Zncent –Biico 282.2(2)–292.8(2), Znico –Biico 287.6(2)–375.5(2), Biico –Biico 320.5(1), Znico –Znico 289.4(2)–376.2(2), Bicap –Znico 259.8(1)–276.8(1), Bicap –Biico 310.7(1)–331.2(1) pm; the subscripts cent, ico, and cap denote atoms occupying the central, icosahedral, and capping sites, respectively.

the negative charges. Note that each vertex Bi atom is considered to retain one lone pair, whereas each capping Bi atom withholds two lone pairs. 15.6.3

Intermolecular interactions in organoantimony and organobismuth compounds

Intermolecular interactions have long been known to exist in inorganic compounds of antimony and bismuth. For example, SbCl3 has three Sb–Cl bonds of length 234 pm and five Sb· · · Cl distances in the range 346–74 pm, thus enlarging the coordination sphere from trigonal pyramidal to (3 + 5) bicapped trigonal prismatic geometry. The organoantimony and organobismuth compounds in oxidation states I–III also exhibit strong intermolecular interactions, which lead to secondary bonds between molecules in forming chain-like, layer-type, and threedimensional supramolecular structures. Figure 15.6.4 shows the structures of three organometallic compounds of Sb and Bi. (1) MeSbCl2 Crystalline MeSbCl2 contains alternating layers, each consisting of double chains of MeSbCl2 molecules. Along a MeSbCl2 chain, the bond lengths and angles are Sb–Cl, 236.8 and 243.0 pm; Sb· · · Cl, 333.7 and 386.5 pm; Sb–Cl· · · Sb (within chain), 102.9◦ . (2) Me2 SbI In the Me2 SbI chain, the bond lengths are Sb–I 279.9 pm and Sb· · · I 366.6 pm, so that the short and long Sb–I bonds are clearly different. The chain atoms lie

607

608

Structural Chemistry of Selected Elements (a)

Sb (b) Sb

I

(c) Br

Bi Fig. 15.6.4.

Structures of organometallic compounds of Sb and Bi: (a) MeSbCl2 , (b) Me2 SbI, (c) MesBiBr2 (Mes = mesityl).

almost in a plane, while the methyl groups are directed to one side of this plane. The reverse side is exposed to neighboring chains with very weak interchain Sb· · · I contacts (402.4–416.7 pm) close to the van der Waals separation. This type of chain packing leads to the formation of double layers. (3) MesBiBr2 In the chain structure of MesBiBr2 , the Bi and bridging Br atoms constitute a zigzag chain, with the nonbridging Br atoms lying on one side and the mesityl groups on the other side of the plane as defined by the positions of the chain atoms. The structure is stabilized by π interaction between the Bi atom and the noncoordinated mesityl group. The bond lengths are Bi–Br, 261.9 and 281.8 pm; Bi· · · Bi, 301.7 and 302.2 pm; Bi– mesityl ring centroid, 319.5 and 330.1 pm. References 1. N. N. Greenwood and A. Earnshaw, Chemistry of the Elements, 2nd edn., Butterworth-Heinemann, Oxford, 1997. 2. R. B. King (ed.), Encyclopedia of Inorganic Chemistry, Wiley, New York, 1994: (a) H. H. Sisler, Nitrogen: Inorganic chemistry, pp. 2516–57; (b) J. R. Lancaster, Nitrogen oxides in biology, pp. 2482–98; (c) J. Novosad, Phosphorus: Inorganic chemistry, pp. 3144–80; (d) R. H. Neilson, Phosphorus–nitrogen compounds, pp. 3180–99. 3. Y. A. Henry, A. Guissani and B. Ducastel, Nitric Oxide Research from Chemistry to Biology: EPR Spectroscopy of Nitrosylated Compounds, Springer, New York, 1997. 4. D. E. C. Corbridge, Phosphorus: An Outline of its Chemistry, Biochemistry and Technology, 5th edn., Elsevier, Amsterdam, 1995.

Group 15 Elements 5. M. Regitz and O. J. Scherer (eds.), Multiple Bonds and Low Coordination in Phosphorus Chemistry, Verlag, Stuttgart, 1990. 6. A. Durif, Crystal Chemistry of Condensed Phosphate, Plenum Press, New York, 1995. 7. K. B. Dillon, F. Mathey and J. F. Nixon, Phosphorus: The Carbon Copy, Wiley, Chichester, 1998. 8. D. E. C. Corbridge, The Structural Chemistry of Phosphorus, Elsevier, Amsterdam, 1974. 9. J. Donohue,The Structure of Elements, Wiley, New York, 1974. 10. M.–T. Averbuch-Pouchot and A. Durif, Topics in Phosphate Chemistry, World Scientific, Singapore, 1996. 11. I. Haiduc and D. B. Sowerby (eds.), The Chemistry of Inorganic Homo- and Heterocycles, vol. 1–2, Academic Press, London, 1987. 12. J.–P. Majoral (ed.), New Aspects in Phosphorus Chemistry I, Springer, Berlin, 2002. 13. G. Meyer, D. Neumann and L. Wesemann (eds.), Inorganic Chemistry Highlights, Wiley–VCH, Weimheim, 2002. 14. S. M. Kauzlarich (ed.), Chemistry, Structure and Bonding of Zintl Phases and Ions, VCH, New York, 1996. 15. M. Gielen, R. Willem and B. Wrackmeyer (eds.), Unusual Structures and Physical Properties in Organometallic Chemistry, Wiley, West Sussex, 2002. 16. H. Suzuki and Y. Matano (eds.), Organobismuth Chemistry, Elsevier, Amsterdam, 2001. 17. K. O. Christe, W. W. Wilson, J. A. Sheehy and J. A. Boatz, N+ 5 : a novel homoleptic polynitogen ion. Angew. Chem. Int. Ed. 38, 2004–9 (1999). 18. B. A. Mackay and M. D. Fryzuk, Dinitrogen coordination chemistry: on the biomimetic borderlands. Chem. Rev. 104, 385–401 (2004). 19. N. Burford and P. J. Ragogna, New synthetic opportunities using Lewis acidic phosphines. Dalton Trans., 4307–15 (2002). 20. E. Urnezius, W. W. Brennessel, C. J. Cramer, J. E. Ellis and P. von R. Schleyer, A carbon-free sandwich complex [(P5 )2 Ti]2− . Science 295, 832–4 (2002). 21. M. Peruzzini, L. Gonsalvia and A. Romerosa, Coordination chemistry and functionalization of white phosphorus via transition metal complexes. Chem. Soc. Rev. 34, 1038–47 (2005). 22. J. G. Cordaro, D. Stein, H. Rüegger and H. Grützmacher, Making the true “CP” ligand. Angew. Chem. Int. Ed. 45, 6159–62 (2006). 23. J. Bai, A. V. Virovets and M. Scheer, Synthesis of inorganic fullerene-like molecules. Science 300, 781–3 (2003). 24. M. J. Moses, J. C. Fettinger and B. W. Eichhorn, Interpenetrating As20 fullerene and Ni12 icosahedra in the onion-skin [As@Ni12 @As20 ]3− ion. Science 300, 778–80 (2003). 25. J. M. Goicoechea and S. C. Sevov, [Zn9 Bi11 ]5− : a ligand-free intermetalloid cluster. Angew. Chem. Int. Ed. 45, 5147–50 (2006).

609

16

Structural Chemistry of Group 16 Elements

16.1

Dioxygen and ozone

Oxygen is the most abundant element on the earth’s surface. It occurs both in the free state and as a component in innumerable compounds. The common allotrope of oxygen is dioxygen (O2 ) or oxygen gas; the other allotrope is ozone (O3 ). 16.1.1

Structure and properties of dioxygen

Molecular oxygen (or dioxygen) O2 and related species are involved in many chemical reactions. The valence molecular orbitals and electronic configurations of the homonuclear diatomic species O2 and O− 2 are shown in Fig. 16.1.1. In the ground state of O2 , the outermost two electrons occupy a doubly degenerate set of antibonding π ∗ orbitals with parallel spins. Dioxygen is thus a paramagnetic molecule with a triplet ground state (3 145.6 pm S – OH 155.8 pm

S – O 149 pm

(b)

(c)

S – Om 164.5 pm <S – Ot> 144 pm S – O – S 124º pm (d)

639

Fig. 16.6.4.

Molecular structure of (a) H2 SO4 , 2− 2− (b) HSO− 4 , (c) SO4 and (d) S2 O7 .

The O–H· · · O hydrogen bond length is 264.8 pm and the bond angle O–H· · · O is 170◦ . The hydrogen sulfate (or bisulfate) anion HSO− 4 exists in crystalline salts such as (H3 O)(HSO4 ), K(HSO4 ) and Na(HSO4 ). The bond lengths of HSO− 4 in (H3 O)(HSO4 ) are S–O = 145.6 pm and S–OH = 155.8 pm. Disulfuric acid (also known as pyrosulfuric acid), H2 S2 O7 , which is the major constituent of “fuming sulfuric acid”, is formed from sulfur trioxide and sulfuric acid: SO3 + H2 SO4 → H2 S2 O7 . Figure 16.6.4(d) shows the structure of the S2 O2− 7 anion.

Y

0

H O2

S O1

X Fig. 16.6.5.

A layer of hydrogen-bonded H2 SO4 molecules.

(2) Sulfurous acid and disulfurous acid Sulfurous acid, H2 SO3 , and disulfurous acid, H2 S2 O5 , are examples of sulfur oxoacids that do not exist in the free state, although numerous salts derived 2− − 2− from them containing the HSO− 3 , SO3 , HS2 O5 , and S2 O5 anions are stable

640

Fig. 16.6.6.

Structural Chemistry of Selected Elements 151

150

2− Structure of (a) SO2− 3 , (b) S2 O5 , and

151

217

239

145

(c) S2 O2− 4 (bond lengths in pm).

solids. An aqueous solution of SO2 , though acidic, contain negligible quantities of the free acid H2 SO3 . The apparent hexahydrate H2 SO3 ·6H2 O is actually the gas hydrate 6SO2 ·46H2 O, in which the SO2 molecules are enclosed in cages within a host framework constructed from hydrogen-bonded water molecules. 2− 2− Figure 16.6.6 shows the structures of the anions SO2− 3 , S2 O5 , and S2 O4 . The − hydrogen sulfite (bisulfite) ion HSO3 has been found to exist in two isomeric − forms: HO–SO− 2 and H–SO3 . (3) Thiosulfate, SSO2− 3 In the thiosulfate ion, a terminal S atom replaces an O atom of the sulfate ion. The S–S bond length is 201.3 pm, which indicates essentially single-bond character, while the mean S–O bond length is 146.8 pm, which indicates considerable π bonding between the S and O atoms. Single-crystal X-ray analysis has shown that the structure of SeSO2− 3 is 2− isostructural with the S2 O3 ion with a Se–S bond length of 217.5(1) pm. The thiosulfate ion, in which the terminal S and O atoms can function as ligand sites, is a polyfunctional species in various coordination modes with metal atoms. Figure 16.6.7 shows the coordination modes of S2 O2− 3 . S

M

S O

Fig. 16.6.7.

The coordination modes of S2 O2− 3 .

(4) Peroxoacids of sulfur The peroxoacids of sulfur and their salts all contain the –O–O– group. The salts of S2 O2− 8 , such as K2 S2 O8 , are very convenient and powerful oxidizing agents. Peroxomonosulfuric acid (Caro’s acid), H2 SO5 , is a colorless, explosive − 2− solid (mp 45◦ C), and salts of HSO− 5 are known. In HSO5 and S2 O8 , the S–O (peroxo) and S–O (terminal) bond distances are different. The S–O (peroxo) bond length is about 160 pm, which corresponds to a single bond, and the S–O (terminal) bond length is about 145 pm, which corresponds to a double bond.

Group 16 Elements

641

2− The structural formulas of HSO− 5 and S2 O8 are shown below: O

HO

O

O

S O

O O

O

S

S

O

O

O

S2O82–

HSO5–

16.7

O

O

Sulfur–nitrogen compounds

Sulfur and nitrogen are diagonally related elements in the Periodic Table and might therefore be expected to have similar electronic charge densities for similar coordination numbers, and to form cyclic, acyclic, and polycyclic molecules through extensive covalent bonding. Some sulfur–nitrogen compounds exhibit interesting chemical bonding and have unusual properties, as discussed below. 16.7.1

Tetrasulfur tetranitride, S4 N4

Nitride S4 N4 is an air-stable compound that can be prepared by passing NH3 gas into a warm solution of S2 Cl2 in CCl4 or benzene. It is a thermochromic crystal: colorless at 83 K, pale yellow at 243 K, orange at room temperature, and deep red above 373 K. The D2d molecular structure of S4 N4 is shown in Fig. 16.7.1(a). The atoms of S4 N4 are arranged so that the electropositive S atoms occupy the vertices of a tetrahedron, while the electronegative N atoms constitute a square that intersects the tetrahedron. All the S–N distances are equal; for gaseous S4 N4 they are 162.3 pm, which is intermediate between the distances of the S–N single bond (174 pm) and S==N double bond (154 pm). The N–S–N bond angle is 105.3◦ , S–N–S is 114.2◦ , and S–S–N is 88.4◦ . A peculiarity of the S4 N4 structure is the short distance between the two S atoms connected by a broken line in Fig. 16.7.1(a); at 258 pm, it lies between the S–S single-bond length (208 pm) and van der Waals contacting distance S· · · S 360 pm. This may imply that the S atom uses two electrons for two σ S–N bonds, one electron for delocalized π bonding, and one electron for S· · · S weak bonding. Tetraselenium tetranitride, Se4 N4 , forms red, hygroscopic crystals and is highly explosive. The structure of Se4 N4 resembles that of S4 N4 with Se–N bond length of 180 pm and cross-cage Se· · · Se distance of 276 pm (note that 2rcov (Se) = 2 × 117pm = 234pm). 258 pm

S

249 pm

As S

N 162 pm (a)

223 pm (b)

Fig. 16.7.1.

Molecular structure of (a) S4 N4 and (b) As4 S4 .

642

Structural Chemistry of Selected Elements (b)

S

N

N

S

N N

S

N

S

S

N

N

S

S

N S

310 S

N

(a) N

N

S

S

Fig. 16.7.2.

Structure of (a) S2 N2 and (b) polymeric chains in one layer of (SN)x and the important structural parameters (bond lengths in pm).

N 162.8 348

S

165

N

S

N 120º

N

S

286

S

106º N

N

S

N

S

N

N

S

N

S

S

N

N S 159.3

S

N N

S

N

N

S

S

S

The homolog realgar, As4 S4 , has an analogous but different structure with the electronegative S atoms at the vertices of a square and the electropositive As atoms at the vertices of a tetrahedron. The As atoms are linked by normal single bonds, as shown by the solid lines between them in Fig. 16.7.1(b). The As–As distance is 249 pm, which is nearly equal to the calculated value of 244 pm (Table 3.4.3). 16.7.2

S2 N2 and (SN)x

When the heated vapor of S4 N4 is passed over silver wool at 520 to 570 K, the unstable cyclic dimer S2 N2 is obtained. It forms large colorless crystals which are insoluble in water but soluble in many organic solvents. The molecular structure of S2 N2 , as shown in Fig. 16.7.2(a), is a D2h squareplanar ring with S–N edge 165 pm, somewhat analogous to the isoelectronic (Fig. 16.4.2). The valence-bond representations of the S2 N2 cation S2+ 4 molecule are as follows: S

N

S

N

S

N

S

N

S

N

N

S

N

S

N

S

N

S

N

S

When colorless S2 N2 crystals are allowed to stand at room temperature, golden (SN)x crystals are gradually formed. The (SN)x chain can conceivably be generated from adjacent square-planar S2 N2 molecules, and a free radical mechanism has been proposed. Since polymerization can take place with only minor movements of the atoms, the starting material and product are pseudomorphs without alteration of the crystallinity. Figure 16.7.2 shows the configuration of the (SN)x chains and the packing of the chains in the crystal. Polymeric (SN)x has some unusual properties. For example, it has a bronze color and metallic luster, and its electrical conductivity is about that of mercury metal. Values of the conductivity of (SN)x depend on the purity and crystallinity of the polymer and on the direction of measurement, being much greater along the fibers than across them. A conjugated single-bond/double-bond system can be formulated, in which every S–N unit has one antibonding π ∗ electron. The half-filled overlapping π ∗ orbitals combine to form a half-filled conduction band, in much the same way as the half-filled ns orbitals of alkali metal atoms

Group 16 Elements

S4N2

S5N6

S11N2

S3N22+

S4N5+

S5N5–

643

Fig. 16.7.3. –

–

N–

S3N3

S4N5

S4

form a conduction band. However, in (SN)x , the conduction band lies only in the direction of the (SN)x fibers, so the polymer behaves as an “one-dimensional metal”. N

S

N N

16.7.3

S

S N

S

Cyclic sulfur–nitrogen compounds

Many cyclic sulfur–nitrogen compounds are known, some of which are shown in Fig. 16.7.3. The general structural features of sulfur–nitrogen compounds are formulated as follows: (a) The S atom has the ability to form various types of S–S and S–N bonds, some of which contain catenated –S–S– chains that can insert into the cyclic chains as a fragment in molecules. For example, the S11 N2 molecule has two S5 chain fragments, and S4 N2 and S4 N− each has one S3 chain fragment. The S· · · S interactions can vary in strength: 314 pm in S4 N− as compared to 271–5 pm in S4 N− 5. (b) The S–N bond distances are in the range of 155 to 165 pm, which are shorter than the calculated single-bond length, so the S–N bonds have some double-bond character. The bond angles vary over a large range: for example,

Structure of some cyclic sulfur–nitrogen compounds (large circle represents S atom and small circle represents N atom).

644

Structural Chemistry of Selected Elements ◦ ◦ in S5 N+ 5 the bond angles are between 138 and 151 . The wide variations of bond distances and angles indicate that the bond types are quite complex. (c) Normally the S and N atoms are each bonded to two adjacent atoms, but in some cases they are also three-connected to form polycyclic molecules. − Some examples are as S5 N6 , S11 N2 , S4 N+ 5 and S4 N5 , the structures of which are shown in Fig. 16.7.3. (d) The conformations of the cyclic S–N molecules exhibit diversity. For − example, S3 N2+ 2 and S3 N3 adopt planar conformations which are stabilized by delocalized π bonding, while the majority of these cyclic molecules are nonplanar, in which the d orbitals of S atoms also participate in bonding.

16.8

Structural chemistry of selenium and tellurium

16.8.1

Allotropes of selenium and tellurium

Selenium forms several allotropes but tellurium forms only one. The thermodynamically stable form of selenium (α-selenium or gray selenium) and the crystalline form of tellurium are isostructural. In both Te and gray Se, the atoms form infinite, helical chains having three atoms in every turn, the axes of which lie parallel to each other in the crystal, as shown in Fig. 16.8.1. The distance of two adjacent atoms within the chain are Se–Se 237 pm and Te–Te 283 pm. Each atom has four adjacent atoms from three different chains at an average distance of Se· · · Se 344 pm, Te· · · Te 350 pm. The interchain distance is significantly shorter than expected from the van der Waals separation (380 pm for Se and 412 pm for Te). Red monoclinic selenium exists in three forms, each containing Se8 rings with the crown conformation of S8 (Fig. 16.4.1). Vitreous black selenium, the ordinary commercial form of the element, comprises an extremely complex and irregular structure of large polymeric rings.

16.8.2

Polyatomic cations and anions of selenium and tellurium

Like their sulfur congener, selenium and tellurium can form polyatomic cations and anions in many compounds. (a)

Fig. 16.8.1.

Structure of α-selenium (or tellurium): (a) side view of Sex (or Tex ) helical chain; (b) viewed along the helices; the hexagonal unit cell and the coordination environment about one atom is indicated.

(b)

Group 16 Elements (a)

(b)

(c)

(d)

(e)

645 Fig. 16.8.2.

Structures of some polyatomic cations of Se and Te. (a) Se2+ 4 in Se4 (H2 S2 O7 )2 ;

2+ Te2+ 4 in Te4 (AsF6 )2 ; (b) Te6 in

(f)

(g)

(h)

Te6 (MOCl4 )2 (M = Nb, W); (c) Te4+ 6 in

(i)

Te6 (AsF6 )4 ·2AsF3 ; (d) Te2+ 8 in

Te8 (ReCl6 )2 ; Se2+ 8 in Se8 (AlCl4 )2 ;

2+ (e) Te2+ 8 in Te8 (WCl6 )2 ; (f) Te8 in

(Te6 )(Te8 )(WCl6 )4 ; (g) Te4+ 8 in

(j)

(k)

(l)

(Te8 )(VOCl4 )2 ; (h) Se2+ 10 in

(m)

Se10 (SbF6 )2 ; (i) Se2+ 17 in Se17 (NbCl6 )2 ;

2+ (j) Se2+ 19 in Se19 (SbF6 )2 ; (k) (Te2 Se4 ) 2+ in (Te2 Se4 )(SbF6 )2 ; (l) (Te2 Se6 ) in (Te2 Se6 )(Te2 Se8 )(AsF6 )4 ; (m) (Te2 Se8 )2+ in (Te2 Se8 )(AsF6 )2 .

(1) Polyatomic cations Figure 16.8.2 show the structures of some polyatomic cations of Se and Te that exist in crystalline salts. Figure 16.8.2(a) shows the square-planar geometry of 2+ the Se2+ 4 and Te4 cations. In Se4 (HS2 O7 )2 the Se–Se distance is 228 pm, and in Te4 (AsF6 )2 the Te–Te distance is 266 pm. These two distances are shorter than those in the respective elemental forms, 237 and 284 pm, respectively, being consistent with the effect of some multiple bonding. _

_ _ +

+

+

+

+

_

+

_

_

_ _ _

+ _ _

+

_

+ +

_

_

+

+

a1′

e′

_

_

+

+

_

_ +

+ + _

_

+ +

_

_ +

+ +

a 2″

_

+

+ _

+ _

+ _

_

+ _

+

+ _

_

+

_ + _ +

Fig. 16.8.3.

e″

The structure of Te4+ 6 is shown in Fig. 16.8.2(c). In this trigonal prismatic cation, the average Te–Te bond length within a triangular face is 268 pm, and the average Te· · · Te distance between the parallel triangular faces is 313 pm. 2+ The Te4+ 6 cation can be considered as a dimer of two Te3 units consolidated ∗ ∗ by a π − π 6c-4e bonding interaction. As shown in Fig. 16.8.3, the tellurium 5pz orbitals give rise to six molecular orbitals of a1, ,e, , a2,, , and e,, symmetry, the first three being used to accommodate eight valence electrons. The e, orbitals are nonbonding within the individual Te2+ 3 units but form bonding interaction between them, and the bonding a1, and antibonding a2,, orbitals cancel each other. The formal bond order along each prism edge is therefore 2/3. 2+ Formal addition of two electrons to Te4+ 6 gives Te6 , which takes the shape of a boat-shaped six-membered ring, as shown in Fig. 16.8.2(b). The average length of the pair of weak transannular interactions is 329 pm, which indicates that the two positive charges are delocalized over all four Te atoms in the rectangular base.

Molecular orbitals in Te4+ 6 .

646

Structural Chemistry of Selected Elements Figure 16.8.2(d) shows the conformation of and weak central transannular 2+ 2+ interaction in the Se2+ 8 and Te8 cations, which are isostructural with S8 . Their common bicyclic structure can be regarded as being derived from a crownshaped eight-membered ring by flipping one atom from an exo to an endo position, with the formally positively charged atoms interacting in transannular linkage. In Te8 (ReCl6 )2 , the Te–Te bond length indicates a normal single bond, and the Te· · · Te distance is 315 pm. In Se8 (AlCl4 )2 , the Se–Se bond lengths lie in the range 229-36 pm, and Se· · · Se is 284 pm. Figures 16.8.2(e) and (f) show two other isomeric forms of Te2+ 8 . In 2+ Te8 (WCl6 )2 , the Te8 cation is composed of two five-membered rings, each taking an envelope conformation, with an average Te–Te bond length of 275 pm and a relatively short transannular Te· · · Te bond of 295 pm. In (Te6 )(Te8 )(WCl6 )4 , Te2+ 8 exhibits a bicyclo[2.2.2]octane geometry with two bridge-head Te atoms. Figure 16.8.2(g) shows the structure of Te4+ 8 ; this 44 valence electron cluster takes a cube shape with two cleaved edges, the positive charges being located on four three-coordinate Te atoms. The Te4+ 8 cation can be viewed as two 2+ planar Te4 ions that have dimerized via the formation of a pair of Te–Te bonds with simultaneous loss of electronic delocalization and distortion from planarity. 2+ 2+ Figures 16.8.2(h), (i), and (j) show the structures of Se2+ 10 , Se17 , and Se19 , respectively. They all consist of seven- or eight-membered rings connected by short chains. Each homopolyatomic cation has two three-coordinate atoms that formally carry the positive charges. Se2+ 10 has a bicyclo[2.2.4]decane geometry. The Se–Se bond distances vary between 225 and 240 pm, and the 2+ Se–Se–Se angles range from 97◦ to 106◦ . Se2+ 17 and Se19 comprise a pair of seven-membered rings connected by a three- and four-atom chain, respectively. Figures 16.8.2(k), (l), and (m) show the structures of (Te2 Se4 )2+ , (Te2 Se6 )2+ and (Te2 Se8 )2+ , respectively. In these heteropolyatomic cations, the heavier Te atoms generally have a higher coordination number of three and serve as positive charge bearers, which is consistent with the lower electronegativity of Te compared to Se. As expected and confirmed by experiment, a weak transannular Te· · · Te bond exists in the boat-shaped (Te2 Se4 )2+ cation. The (Te2 Se6 )2+ and (Te2 Se8 )2+ cations have bicyclo[2.2.2]octane and bicyclo[2.2.4]decane geometries, respectively, with the Te atoms located at the bridge-head positions. Figure 16.8.4 shows the structures of some polymeric cations of Se and Te. In most of these systems, the Te–Te bonds link the Te atoms to form an infinite polymeric chain. The coordination numbers of the Te atoms are normally two or three, but some may attain the value of four in forming hypervalent structures. Various polymeric cations contain four-, five-, or six-membered rings. The four-membered ring is planar, but the larger rings are nonplanar. The rings are directly connected or linked by short fragments of one, two, three atoms. In the heteroatom polymeric cations, the Te atoms invariably occupy the threecoordinate sites. Figures 16.8.4(a) and (j) show the structures of the coexisting (Te2+ 4 )∞ and 2+ ) in (Te )(Te )(Bi Cl ). (Te ) is composed of planar squares of (Te2+ ∞ 4 10 4 16 ∞ 10 4 Te atoms connected by Te–Te bonds to form an infinite zigzag chain. There are

Group 16 Elements (a)

(c)

(e)

647

(b)

(d)

(f) Fig. 16.8.4.

(g)

(h)

Structures of some polymeric cations of Se and Te. (a) (Te2+ 4 )∞ in

(Te4 )(Te10 )(Bi4 Cl16 ), (b) (Te2+ 6 )∞ in (Te6 )(HfCl6 ), (c) (Te2+ 7 )∞ in

(i)

(j)

(Te7 )(AsF6 )2 , (d) (Te2+ 8 )∞ in

(Te8 )(U2 Br10 ), (e) (Te2+ 8 )∞ in

(Te8 )(Bi4 Cl14 ), (f) (Te3.15 Se2+ 4.85 )∞ in (Te3.15 Se4.85 )(WOCl4 )2 , (g) (Te3 Se2+ 4 )∞ in (Te3 Se4 )(WOCl4 )2 , (h) (Te2+ 7 )∞ in (Te7 )(Bi2 Cl6 ),

(i) (Te2+ 7 )∞ in (Te7 )(NbOCl4 )2 , and

(j) (Te2+ 10 )∞ in (Te4 )(Te10 )(Bi4 Cl16 ).

equal numbers of two- and three-coordinate Te atoms, so that the latter carry the positive charges. The bond lengths within each square ring are 275 and 281 pm, and the interring bond distance is 297 pm. Figures 16.8.4(b) to (e) show the structures of (Te2+ 6 )∞ in (Te6 )(HfCl6 ), 2+ ) in (Te )(AsF ) , and (Te ) in (Te )(U Br (Te2+ 7 6 2 8 2 10 ) and (Te8 )(Bi4 Cl14 ), 7 ∞ 8 ∞ respectively. These polymeric zigzag chains are composed of five- or sixmembered rings linked by one or two atoms. Figures 16.8.4(f) and (g) show the structures of two related heteroatom polymeric cationic chains composed of Te and Se. In (Te3.15 Se4.85 )(WOCl4 )2 , the non-stoichiometric, disordered (Te3.15 Se2+ 4.85 )∞ cationic chains are constructed from the linkage of five-membered rings by nonlinear three-atom fragments. In (Te3 Se4 )(WOCl4 )2 , the (Te3 Se2+ 4 )∞ chain is composed of planar Te2 Se2 rings connected by nonlinear Se–Te–Se fragments. Figures 16.8.4(h) to (j) show the structures of polymeric cations that contain hypervalent Te atoms. Two kinds of (Te2+ 7 )∞ chains are found separately in (Te7 )(Bi2 Cl6 ) and (Te7 )(NbOCl4 )2 , and (Te2+ 10 )∞ exists in (Te4 )(Te10 )(Bi4 Cl16 ). In these polymeric cations, the hypervalent Te atoms each exhibits square-planar coordination to form a TeTe4 unit with Te–Te bond lengths in the range 292–7 pm. In (Te2+ 7 )∞ , the TeTe4 unit and a pair of terminal Te atoms constitute an enlarged Te7 unit composed of two planar squares sharing a common vertex. In (Te2+ 10 )∞ , the basic Te10 structural unit consists of a linear arrangement of three corner-sharing planar squares, and such Te10

648

Structural Chemistry of Selected Elements

Se42–

Se52–

Se62–

Se72–

Se92–

Se112–

Fig. 16.8.5.

Structures of some dianions Se2− x . For Se2− , the longest bond is represented by 9 a broken line.

units are laterally connected by Te–Te bonds to generate a corrugated polymeric ribbon that also contain chair-like six-membered rings. (2) Polyatomic anions The chemistry of polyselenides, polytellurides, and their metal complexes is very well established. Typical structures of polyselenide dianions are shown in Fig. 16.8.5. In these species, the Se–Se bond distances vary from 227 to 236 pm, and the bond angles from 103◦ to 110◦ . The tethered monocyclic structure of Se2− 9 in the complex Sr(15-C5)2 (Se9 ) has a three-connected Se atom forming two long and one normal Se–Se bonds at 295, 247, and 231 pm (anticlockwise in Fig. 16.8.5, with the longest bond represented by a broken line). The other Se–Se bonds are in the range 227–39 pm.

Te42–

Te32–

Fig. 16.8.6.

Structures of some dianions Te2− x .

Te72–

Te52–

Te82–

The dianion Se2− 11 has a centrosymmetric spiro-bicyclic structure involving a central square-planar Se atom common to the two chair-shaped rings. The shared atom forms four long Se–Se bonds of length 266–8 pm, and the structure may be described as a central Se2+ chelated by two η2 -Se2− 5 ligands. Some typical structures of polytelluride dianions, Te2− x , are shown in Fig. 16.8.6. In these species, the Te–Te bond distances vary from 265 to 284 pm. 2− In the bicyclic polytellurides Te2− 7 and Te8 , the central Te atom each has four long bonds with bond lengths from 292 to 311 pm. 2− The Se2− x and Tex are effective chelating ligands for both main group 2 and transition metals, giving rise to complexes such as Sn(η2 -Se4 )2− 3 , [M(η 2− 5 2 3 2− Se4 )2 ] (M = Zn, Cd, Hg, Ni, Pb), Ti(η -C5 H5 )2 (η -Se5 ), [Hg(η -Te7 )] , and M2 (µ2 -Te4 )(η2 -Te4 )2 (M = Cu, Ag).

Group 16 Elements 16.8.3

Stereochemistry of selenium and tellurium

Selenium and tellurium exhibit a great variety of molecular geometries as a consequence of the number of stable oxidation states. Various observed structures are summarized in Table 16.8.1, in which A is a central Se or Te atom, X is an atom bonded to A, and E represents a lone pair. Table 16.8.1. Molecular geometries of Se and Te

Type

Molecular geometry

Example (structure in Fig. 16.8.7)

AX2 E AX2 E2 AX3 AX3 E

Bent Bent Trigonal planar Trigonal pyramidal T-shaped Tetrahedral Disphenoidal Square pyramidal Octahedral Octahedral Pentagonal bipyramidal

SeO2 SeCl2 , Se(CH3 )2 , TeCl2 , Te(CH3 )2 SeO3 , TeO3 (SeO2 )x (a), OSeF2 (b)

AX3 E2 AX4 AX4 E AX5 E AX6 AX6 E AX7

[SeC(NH2 )2 ]2+ 3 (c), C6 H5 TeBr(SC3 N2 H6 ) (d) O2 SeF2 , (SeO3 )4 Se(C6 H5 )2 Cl2 , Se(C6 H5 )2 Br2 , Te(CH3 )2 Cl2 , Te(C6 H5 )2 Br2 TeF− 5 (e), (TeF4 )x (f) SeF6 , TeF6 , (TeO3 )x , F5 TeOTeF5 (g) 2− SeCl2− 6 , TeCl6 TeF− (h) 7

With reference to Table 16.8.1, the stereochemistries of Se and Te compounds are briefly described below. (1) AX2 E type The SeO2 molecule in the vapor phase has a bent configuration with Se–O 160.7 pm and O–Se–O 114◦ . Crystalline SeO2 is built of infinite chains, in which each Se atom is bonded to three oxygen atoms (AX3 E type) in a trigonal pyramidal configuration. The bond lengths are Se–Ob 178 pm, Se–Ot 173 pm, as shown in Fig. 16.8.7(a). (2) AX2 E2 type Many AX2 E2 type molecules, such as Se(CH3 )2 , SeCl2 , Te(CH3 )2 , and TeBr2 , all exhibit a bent configuration, in which repulsion of lone pairs makes the interbond angles smaller than the ideal tetrahedral angle: A–X (pm) X–A–X

Se(CH3 )2 194.5 96.3◦

SeCl2 215.7 99.6◦

Te(CH3 )2 214.2 94◦

TeCl2 232.9 97◦

(3) AX3 type Monomeric selenium trioxide (SeO3 ) and tellurium trioxide (TeO3 ) have a trigonal planar structure in the gas phase. In the solid state, SeO3 forms cyclic tetramers (SeO3 )4 , in which each Se atom connects two bridging O atoms and two terminal O atoms, with Se–Ob 177 pm and Se–Ot 155 pm (AX4 type).

649

650

Structural Chemistry of Selected Elements Se

Se O

O F

(a)

(b)

N Te

S

Se

Br

C NH2

(d)

(c)

Te

Te F

(e)

O

(f)

Te Te

F

F

Fig. 16.8.7.

Stereochemistry of Se and Te compounds.

(g)

(h)

The solid-state structure of TeO3 is a three-dimensional framework, in which Te(VI) forms TeO6 octahedra (AX6 type) sharing all vertices. (4) AX3 E type Pyramidal molecule SeOF2 has bond lengths Se=O 158 pm and Se–F 173 pm, bond angles F–Se–F 92◦ and F–Se–O 105◦ , as shown in Fig. 16.8.7(b). Its dipole moment (2.62 D in benzene) and dielectric constant (46.2 at 20◦ C) are both high, and accordingly it is a useful solvent. (5) AX3 E2 type The cation [SeC(NH2 )2 ]2+ adopts T-shaped geometry, as shown in 3 Fig. 16.8.7(c). In this structure, the central Se atom must bear a formal negative charge to have two lone pairs at the equatorial positions of a trigonal bipyramid.

Group 16 Elements The valence-bond structural formula of this cation is given below: +

H2N

NH2

C Se +

Se

–

Se

C

H2N

C

NH2 H2N

+

NH2

In the molecule C6 H5 TeBr(SC3 N2 H6 ), the Te atom has a similar T-shaped configuration, as shown in Fig. 16.8.7(d). Bonding can be described in terms of resonance between a pair of valence-bond structures: H2C H2C

+ NH

H2C H2C

C N H

S

− Te

C +N H

Br

C6H5

NH

S

− Te Br C6H5

(6) AX4 type The molecule SeO2 F2 and analogous compounds have tetrahedral geometry with three different bond angles: O–Se–O 126.2◦ , O–Se–F 108.0◦ , and F–Se–F 94.1◦ . (7) AX4 E type The molecules Se(C6 H5 )2 Cl2 , Se(C6 H5 )2 Br2 , Te(CH3 )2 Cl2 , and Te(C6 H5 )2 Br2 constitute this structure type. In all these molecules, the halogen atoms occupy the axial positions, as shown below: X Te X

C6H5 C6H5

(8) AX5 E type The anion TeF− 5 and polymeric (TeF4 )x belong to the AX5 E type with squarepyramidal configuration. In TeF− 5 , the bonds in the square base (196 pm) are longer than the axial bond (185 pm), and the bond angles (79◦ ) are smaller than 90◦ , as shown in Fig. 16.8.7(e). Crystalline (TeF4 )x has a chain structure, in which TeF5 groups are linked by bridging F atoms in such a way that alternate pyramids are oriented in opposite directions, as shown in Fig. 16.8.7(f). (9) AX6 type The hexafluorides SeF6 and TeF6 have the expected regular octahedral configuration. In F5 SeOSeF5 and F5 TeOTeF5 , the Se and Te atoms take the octahedral configuration, and the four equatorial bonds in each case are bent away from the bridging O atom, as shown in Fig. 16.8.7(g).

651

652

Structural Chemistry of Selected Elements (10) AX6 E type 2− The anions SeX2− 6 and TeX6 (X = Cl, Br) adopt regular octahedral geometry, apparently indicating that the lone pair in the valence shell is stereochemically inactive. The observed result can be explained as follows. (a) With increasing size of the central atom the tendency for the lone pair to spread around the core is enhanced. It is drawn inside the valence shell, behaving like an s-type orbital and effectively becoming the outer shell of the core. (b) This tendency is also enhanced by the presence of six bonding pairs in the valence shell, which leaves rather little space for the lone pair. (c) With the addition of the nonbonding electron pair, the core size increases and the core charge decreases from +6 to +4, with the result that the bond pairs move farther from the central nucleus, thus increasing the bond lengths. In accordance with this, the observed bond lengths of SeX2− 6 , 2− 2− TeX6 , and SbX6 (X = Cl, Br) ions are considerably longer than those expected from the sum of the covalent radii by about 20-5 pm. (11) AX7 type The TeF− 7 ion, an isoelectronic and isostructural analog of IF7 , has a pentagonal bipyramidal structure with Te–Fax 179 pm and Te–Feq 183-90 pm, as shown in Fig. 16.8.5(h). The equatorial F atoms deviate slightly from the mean equatorial plane.

References 1. N. N. Greenwood and A. Earnshaw, Chemistry of the Elements, 2nd edn., Butterworth-Heinemann, Oxford, 1997. 2. D. F. Shriver, P. W. Atkins, T. L. Overton, J. P. Rourke, M. T. Weller and F. A. Armstrong, Inorganic Chemistry, 4th edn., Oxford University Press, Oxford, 2006. 3. R. B. King, Inorganic Chemistry of Main Group Elements, VCH, New York, 1995. 4. J. Gillespie and I. Hargittai, The VSEPR Model of Molecular Geometry, Allyn and Bacon, Boston, 1991. 5. J. Donohue, The Structure of the Elements, Wiley, New York, 1974. 6. U. Müller, Inorganic Structural Chemistry, 2nd edn., Wiley, Chichester, 2006. 7. K. Kuchitsu (ed.), Structure of Free Polyatomic Molecules: Basic Data, Springer, Berlin, 1998. 8. R. B. Kings (ed.), Encyclopedia of Inorganic Chemistry, Wiley, New York, 1994: (a) R. R. Conry and K. D. Karlin, Dioxygen and related ligands, pp. 1036–40; (b) D. T. Sawyer, Oxygen: inorganic chemistry, pp. 2947–88; (c) J. D. Woolins, Sulfur: inorganic chemistry, pp. 3954–88; (d) T. Chivers, Sulfur-nitrogen compounds, pp. 3988–4009. 9. D. T. Sawyer, Oxygen Chemistry, Oxford University Press, Oxford, 1991. 10. C. S. Foote, J. S. Valentine, A. Greenberg and J. F. Liebman (eds.), Active Oxygen in Chemistry, Blackie, London, 1995. 11. A. E. Martell and D. T. Sawyer (eds.), Oxygen Complexes and Oxygen Activation by Transition Metal Complexes, Plenum Press, New York, 1988.

Group 16 Elements 12. I. Haiduc and D. B. Sowerby (eds.), The Chemistry of Inorganic Homo- and Heterocycles, Vol. 1-2, Academic Press, London, 1987. 13. R. Steudel (ed.), The Chemistry of Inorganic Ring Systems, Elsevier, Amsterdam, 1992. 14. T. Chivers, A Guide to Chalcogen-Nitrogen Chemistry, World Scientific, Singapore, 2005. 15. E. I. Stiefel and K. Matsumoto (eds.), Transitional Metal Sulfur Chemistry: Biological and Industrial Significance, American Chemical Society, Washington, DC, 1996. 16. J.-X. Lu (ed.), Some New Aspects of Transitional-Metal Cluster Chemistry, Science Press, Beijing/New York, 2000. 17. L. F. Lundegaard, G. Weck, M. I. McMahon, S. Desgreniers and P. Loubeyre, Observation of an O8 molecular lattice in the ε phase of solid oxygen. Nature 443, 201–4 (2006). 18. H. Pernice, M. Berkei, G. Henkel, H. Willner, G. A. Argüello, H. L. McKee and T. R. Webb, Bis(fluoroformyl)trioxide, FC(O)OOOC(O)F. Angew. Chem. Int. Ed. 43, 2843–6 (2004). 19. T. S. Zwier, The structure of protonated water clusters. Science 304, 1119–20 (2004). 20. M. Miyazaki, A. Fujii, T. Ebata and N. Mikami, Infrared spectroscopic evidence for protonated water clusters forming nanoscale cages. Science 304, 1134–7 (2004). 21. J.-W. Shin, N. I. Hammer, E. G. Diken, M. A. Johnson, R. S. Walters, T. D. Jaeger, M. A. Duncan, R. A. Christie and K. D. Jordan, Infrared signature of structures associated with the H+ (H2 O)n (n = 6 to 27) clusters. Science 304, 1137–40 (2004). 22. R. Steudel, K. Bergemann, J. Buschmann and P. Luger, Application of dicyanohexasulfane for the synthesis of cyclo-nonasulfur. Crystal and molecular structures of S6 (CN)2 and of α-S9 . Inorg. Chem. 35, 2184–8 (1996). 23. R. Steudel, O. Schumann, J. Buschmann and P. Luger, A new allotrope of elemental sulfur: convenient preparation of cyclo-S14 from S8 . Angew. Chem. Int. Ed. 37, 2377–8 (1998). 24. J. Beck, Polycationic clusters of the heavier group 15 and 16 elements, in G. Meyer, D. Naumann and L. Wesemann (eds.), Inorganic Chemistry in Focus II, Wiley–VCH, Weinheim, 2005, pp. 35–52. 25. W. S. Sheldrick, Cages and clusters of the chalcogens, in M. Driess and H. Nöth (eds.), Molecular Clusters of the Main Group Elements, Wiley-VCH, Weinheim, 2004, pp. 230–45.

653

17

Structural Chemistry of Group 17 and Group 18 Elements 17.1

Elemental halogens

17.1.1

Crystal structures of the elemental halogens

The halogens are diatomic molecules, whose color increases steadily with atomic number. Fluorine (F2 ) is a pale yellow gas, bp 85.0 K. Chlorine (Cl2 ) is a greenish-yellow gas, bp 239.1 K. Bromine (Br2 ) is a dark-red liquid, bp 331.9 K. Iodine (I2 ) is a lustrous black crystalline solid, mp 386.7 K, which sublimes and boils readily at 458.3 K. Actually solid iodine has a vapor pressure of 41 Pa at 298 K and 1.2 × 104 Pa at the melting point. In the solid state, the halogen molecules are aligned to give a layer structure. Fluorine exists in two crystalline modifications: a low-temperature α-form and a higher temperature β-form, neither of which resembles the orthorhombic layer structure of the isostructural chlorine, bromine, and iodine crystals. Figure 17.1.1 shows the crystal structure of iodine. Table 17.1.1 gives the interatomic distances in gaseous and crystalline halogens. The molecules F2 , Cl2 , and Br2 in the crystalline state have intramolecular distances (X–X) which are nearly the same as those in the gaseous state. In crystalline iodine, the intramolecular I–I bond distance is longer than that in a gaseous molecule, and the lowering of the bond order is offset by the intermolecular bonding within each layer. The closest interatomic distance between neighboring I2 molecules is 350 pm, which is considerably shorter than twice the van der Waals radius (430 pm). It therefore seems that appreciable secondary bonding interactions occur between the iodine molecules, giving rise to the semiconducting properties and metallic luster; under very high pressure iodine becomes a metallic conductor. The distance between layers in the iodine crystal (427 and 434 pm) corresponds to the van der Waals distance.

17.1.2

Homopolyatomic halogen anions

The homopolyhalogen anions are formed mainly by iodine, which exhibits the highest tendency to form stable catenated anionic species. Numerous examples 2− − of small polyiodides, such as I− 3 , I4 and I5 , and extended discrete oligomeric − 2− − 2− 2− 4− 4− anionic polyiodides, such as I7 , I8 , I9 , I12 , I16 , I16 , I22 and I3− 29 , and poly− meric (I7 )n networks have been reported. These polyiodides are all formed by the relatively loose association of several I2 molecules with several I− and/or I− 3

Group 17 and Group 18 Elements

655

427 pm

434 pm 350 p

m

272 pm

m 50 p

3

Fig. 17.1.1.

Crystal structure of iodine.

anions. In order to assess the association of such species, the following equation between the bond length (d ) and bond order (n) has been proposed: d = do − c log n = 267 pm − (85 pm) log n. In this equation, the reference I–I single-bond length do is taken to be 267 pm; when the distance d between two iodine atoms is ≤ 293 pm, corresponding to bond order n ≥ 0.50, there is a relatively strong bond between them, which is represented by a solid line. The distance d between 293 and 352 pm corresponds to bond order n between 0.50 and 0.10, indicating a relatively weak bond, which is represented by a broken line. When the distance is longer than 352 pm, there is only van der Waals interaction between the two molecular/ionic species, and no discrete polyiodide is formed. Table 17.1.1. Interatomic distances in gaseous and crystalline halogens

X· · · X (pm)

X–X (pm) X F Cl Br I

Gas

Solid

Within layer

Between layers

143.5 198.8 228.4 266.6

149 198 227 272

324 332 331 350

284 374 399 427

Ratio

X· · ·X (Shortest) X-X (Solid) 1.91 1.68 1.46 1.29

Figure 17.1.2 shows some polyiodides, which have been characterized structurally. All polyiodine anions consist of units of I− , I2 , and I− 3 . The bond length of the structural components of the polyiodides are often characteristic: 267 to 285 pm in I2 molecular fragments, whereas those of symmetrical triiodide I− 3 are about 292 pm. The formation and stability of an extended polyiodide species are dependent on the size, shape, and charge of its accompanying cation. In the solid state, the polyiodide species are assembled around a central cation to form a discrete or one-, two-, or three-dimensional structure.

656

Structural Chemistry of Selected Elements (a)

(b) (c)

290

290

283

303

280

334

(d)

304 339 277

334 (e)

315

301

283

(f)

328 329

281

280

284

305

273

274

(g)

343

267

324

267

318

(h)

303

284

345

335

290

276

324 291

Fig. 17.1.2.

(i) 350

272

Structures of some polyiodides: (a) I− 3 (symmetric) in Ph4AsI3 , (b) I− 3 (asymmetric) in CsI3 , (c) I2− 4 in Cu(NH3 )4 I4 , (d) I− in Fe(S 2 CNEt2 )3 I5 , 5 2− (e) I− in Ph PI , (f) I in [(CH 4 7 2 )6 N4 7 8 4− Me]2 I8 , (g) I− in Me NI , (h) I 4 9 9 16 in [(C7 H8 N4 O2 )H]4 I16 , (i) I2− in 16 (Cp*2 Cr2 I3 )2 I16 , and ( j) (I− 7 )n network in a unit cell of the {Ag[18]aneS6 }I7

342 279 311 332

292

(j) 274

338

336

273

273

294

275

340 339

312 217 334 274

complex. Bond lengths are in pm.

17.1.3

Homopolyatomic halogen cations

The structures of the following homopolyatomic halogen cations have been determined by X-ray analysis: X+ 2: X+ 3:

+ + + − − Br+ 2 and I2 (in Br2 [Sb3 F16 ] and I2 [Sb2 F11 ] ) + + + Cl3 , Br3 and I3 (in X3AsF6 )

2+ 2+ − − X2+ 4 : I4 (in I4 [Sb3 F16 ] [SbF6 ] ) + + + X5 : Br5 and I5 (in X5AsF6 ) X+ I+ 15 : 15 (in I15AsF6 )

+ + 1 X+ 2 : The bond lengths of Br2 and I2 , with a formal bond order of 1 /2, are 215 and 258 pm, respectively, which are shorter than the bond lengths of

Group 17 and Group 18 Elements

657

molecular Br2 (228 pm) and I2 (267 pm). This is consistent with the loss of an electron from an antibonding orbital. These cations have a bent structure (Fig. 17.1.3(a)). The X–X bond lengths are similar to those in gaseous X2 , being consistent with their single-bond character. The bond angles are between the 101◦ and 104◦ . Compound I4 [Sb3 F16 ][SbF6 ] contains an I2+ 4 cation, which has the shape of a planar rectangle with I–I bond lengths of 258 and 326 pm, as shown in Fig. 17.1.3(b). + Cations Br+ 5 and I5 are iso-structural, as shown in Fig. 17.1.3(c). Compound I15AsF6 contains an I+ 15 cation, which has the shape of a centrosymmetric zigzag chain. This cation may be considered to be a finite zigzag chain composed of three connected I− 5 units, as shown in Fig. 17.1.3(d).

X+ 3: X2+ 4 : X+ 5: X+ 15 :

326 266

267

290

258

265 (a)

(c)

(b) 270 i 290

290 Fig. 17.1.3.

342 268

292

267

(d)

17.2

Interhalogen compounds and ions

The halogens form many compounds and ions that are binary or ternary combinations of halogen atoms. There are three basic types: (a) neutral interhalogen compounds, (b) interhalogen cations, and (c) interhalogen anions. 17.2.1

Neutral interhalogen compounds

The halogens react with each other to form binary interhalogen compounds XY, XY3 , XY5 and XY7 , where X is the heavier halogen. A few ternary compounds are also known, e.g., IFCl2 and IF2 Cl. All interhalogen compounds contain an even number of halogen atoms. Table 17.2.1 lists the physical properties of some XYn compounds. XY: All six possible diatomic interhalogen compounds between F, Cl, Br and I are known, but IF is unstable, and BrCl cannot be isolated free from Br2 and Cl2 . In general, the diatomic interhalogens exhibit properties intermediate

Structures of some polyiodine cations: 2+ + + (a) I+ 3 , (b) I4 , (c) I5 and (d) I15 . Bond + lengths are in pm. Both I5 and I+ 15 are centrosymmetric.

658

Structural Chemistry of Selected Elements Table 17.2.1. Physical properties of some interhalogen compounds

Compound

Appearance at 298 K

mp (K)

ClF BrF BrCl ICl (α) ICl (β) IBr ClF3 BrF3 IF3 (ICl3 )2 ClF5 BrF5 IF5 IF7

Colorless gas Pale brown gas Red brown gas Ruby red crystal Brownish red crystal Black crystal Colorless gas Yellow liquid Yellow solid Orange solid Colorless gas Colorless liquid Colorless liquid Colorless gas

117 240 — 300 287 314 197 282 245 (dec) 337 (sub) 170 212.5 282.5 278 (sub)

bp(K) 173 293 — ∼ 373 — ∼ 389 285 399 — — 260 314 378 —

Bond length*(pm) 163 176 214 237, 244 235, 244 249 160 (eq) 170 (ax) 172 (eq) 181 (ax) — 238 (t) 268 (b) 172 (ba) 162 (ap) 172 (ba) 168 (ap) 189 (ba) 186 (ap) 186 (eq) 179 (ax)

* The XY3 molecule has a T-shaped structure: axial (ax), equatorial (eq); (ICl3 )2 is a dimer: bridging (b), terminal (t); XY5 forms a square-based pyramid: apical (ap), basal (ba); XY7 has the shape of a pentagonal bipyramid: equatorial (eq), axial (ax).

between their parent halogens. However, the electronegativities of X and Y differ significantly, so the X–Y bond is stronger than the mean of the X–X and Y–Y bond strengths, and the X–Y bond lengths are shorter than the mean of d (X–X) and d (Y–Y). The dipole moments for polar XY molecules in the gas phase are ClF 0.88 D, BrF 1.29 D, BrCl 0.57 D, ICl 0.65 D, and IBr 1.21 D. Iodine monochloride ICl is unusual in forming two modifications: the stable α-form and the unstable β-form, both of which have infinite chain structures and significant I···Cl intermolecular interactions of 294 to 308 pm. Figure 17.2.1(a) shows the chain structure of β-ICl. XY3 : Both ClF3 and BrF3 have a T-shaped structure, being consistent with the presence of 10 electrons in the valence shell of the central atom, as shown in Fig. 17.2.1(b). The relative bond lengths of d (X–Yax ) > d (X–Yeq ) and the bond angle of Yax –X–Yeq < 90◦ (ClF3 87.5◦ and BrF3 86◦ ) reflect the greater electronic repulsion of the nonbonding pair of electrons in the equatorial plane of the molecule. Iodine trichloride is a fluffy orange powder that is unstable above room temperature. Its dimer (ICl3 )2 has a planar structure, as shown in Fig. 17.2.1(c), that contains two I–Cl–I bridges (I–Cl distances in the range of 268–272 pm) and four terminal I–Cl bonds (238–9 pm). XY5 : The three fluorides ClF5 , BrF5 , and IF5 are the only known interhalogens of the XY5 type, and they are extremely vigorous fluorinating reagents. All three compounds occur as a colorless gas or liquid at room temperature. Their structure has been shown to be square pyramidal with the central atom slightly below the plane of the four basal F atoms [Fig. 17.2.1(d)]. The bond angles F(ap) –X–F(ba) are ∼90◦ (ClF5 ), 85◦ (BrF5 ) and 81◦ (IF5 ). XY7 : IF7 is the sole representative of this structural type. Its structure, as shown in Fig. 17.2.1(e), exhibits a slight deformation from pentagonal

Group 17 and Group 18 Elements ax

244 294

eq

Cl

306 I

235

Cl

F

(a)

(b) ax

ap b 94º

ba

t

84º I

I

Cl

F

I

eq

(c)

(e)

(d)

bipyramidal D5h symmetry due to a 7.5◦ puckering and a 4.5◦ axial bending displacement. Bond length I–F(eq) is 185.5 pm and I–F(ax) is 178.6 pm. Interhalogen ions

− These ions have the general formulas XY+ n and XYn , where n can be 2, 4, 5, 6, and 8, and the central halogen X is usually heavier than Y. Table 17.2.2 lists many of the known interhalogen ions. Table 17.2.2. Some interhalogen ions

XY2 Cations

Anions

ClF+ 2 Cl2 F+ BrF+ 2 IF+ 2 ICl+ 2

BrCl− 2 Br2 Cl− I2 Cl− FClF− FIBr−

I2 Cl+ IBr+ 2 I2 Br+ IBrCl+ ClICl− ClIBr− BrIBr−

ClF− 4 BrF− 4 IF− 4 ICl3 F− ICl− 4 IBrCl− 3

XY4

XY5

XY6

XY8

ClF+ 4 BrF+ 4 IF+ 4 I3 Cl+ 2

—

ClF+ 6 BrF+ 6 IF+ 6

—

IF2− 5

ClF− 6 BrF− 6 IF− 6

IF− 8

I2 Cl− 3 I2 BrCl− 2 I2 Br2 Cl− I2 Br− 3 I4 Cl−

Fig. 17.2.1.

Structures of some interhalogen molecules: (a) β-ICl, (b) ClF3 , (c) I2 Cl6 , (d) IF5 , and (e) IF7 .

F

17.2.2

659

The structures of these ions normally conform to those predicted by the VSEPR theory, as shown in Fig. 17.2.2. Since the anion XY− n has two more , they have very different shapes. The anion electrons than the cation XY+ n IF2− is planar with lone pairs occupying the axial positions of a pentagonal 5 bipyramid. In [Me4 N](IF6 ), IF− 6 is a distorted octahedron (C3v symmetry) with − a sterically active lone pair, whereas both BrF− 6 and ClF6 are octahedral. The anion IF− 8 has the expected square antiprismatic structure.

660

Structural Chemistry of Selected Elements

I2Cl+ 8 electrons

IF4+ 10 electrons

IF6+ 12 electrons

IF4– 12 electrons

IF52– 14 electrons

IF6– 14 electrons

I2Cl– 10 electrons

Fig. 17.2.2.

Structures of some interhalogen ions. The number of electrons in the valence shell of the central atom is given for each ion.

17.3

IF8– 16 electrons

Charge-transfer complexes of halogens

A charge-transfer (or donor–acceptor) complex is one in which a donor and an acceptor species interact weakly with some net transfer of electronic charge, usually facilitated by the acceptor. The diatomic halogen molecule X2 has HOMO π ∗ and LUMO σ ∗ molecular orbitals, and the σ * orbital is antibonding and acts as an acceptor. If the X2 molecule is dissolved in a solvent such as ROH, H2 O, pyridine, or CH3 CN that contains N, O, S, Se, or π electron pairs, the solvent molecule can function as a donor through the interaction of one of its σ or π electron pairs with the σ ∗ orbital of X2 . This donor–acceptor interaction leads to the formation of a charge-transfer complex between the solvent (donor) and X2 (acceptor) and alters the optical transition energy of X2 , as shown in Fig. 17.3.1. Let us take I2 as an example. The normal violet color of gaseous iodine is attributable to the allowed π ∗ → σ ∗ transition. When iodine is dissolved in a solvent, the interaction of I2 with a donor solvent molecule causes an increase in the energy separation of the π ∗ to σ ∗ orbitals from E1 to E2 , as shown in Fig. 17.3.1. The color of this solution is then changed to brown. (The absorption maximum for the violet solution occurs at 520 to 540 nm, and that of a typical brown solution at 460 to 480 nm.) The electron transition in these I2 · solvent complexes is called a charge-transfer transition. However, the most direct evidence for the formation of a charge-transfer complex in solution comes from the appearance of an intense new charge-transfer band occurring in the near ultraviolet spectrum in the range 230–330 nm. The structures of many charge-transfer complexes have been determined. All the examples shown in Fig. 17.3.2 share the following common structural characteristics:

Group 17 and Group 18 Elements

σ*

661

E2 E1

π*

σ or π

X2

Fig. 17.3.1.

solvent

X2 solvent complex

Interaction between the σ ∗ orbital of X2 and a donor orbital of solvent.

(a) The donor atom (D) or π orbital (π) and X2 molecule are essentially linear: D · · · X–X or π · · · X–X. (b) The bond lengths of the X–X groups in the complexes are all longer than those in the corresponding free X2 molecules; the D· · · X distance is invariably shorter than the sum of their van der Waals radii. (c) Each X2 molecule in an infinite chain structure is engaged by donors (D) at both ends, and the D · · · X–X · · · D unit is essentially linear, as expected for a σ -type acceptor orbital.

233 H

N

284

Br (a)

291 I

336

376

228 Se

Br

(d)

(b)

Fig. 17.3.2.

O

283

327

X

N

I

(c)

(e)

In the extreme case, complete transfer of charge may occur, as in the formation of [I(py)2 ]+ : 2I2 + 2

N

N

+ I

_

N

+ I3

Structures of some charge-transfer complexes (bond lengths in pm). (a) (H3 CCN)2 ·Br2 , (b) C6 H6 ·Br2 , (c) C4 H8 O2 ·X2 (X = Cl, Br, X–X distance: 202 pm for X = Cl and 231 pm for X = Br), (d) C4 H8 Se·I2 , and (e) Me3 N·I2 .

662

Structural Chemistry of Selected Elements 17.4

Halogen oxides and oxo compounds

17.4.1

Binary halogen oxides

The structures of some binary halogen oxides are listed in Table 17.4.1. (1) X2 O molecules (a) Since fluorine is more electronegative than oxygen, the binary compounds of F2 and O2 are named oxygen fluorides, rather than fluorine oxides. F2 O is a colorless, highly toxic, and explosive gas. The molecule has C2v symmetry, as expected for a molecule with 20 valence electrons and two normal single bonds. (b) Dichlorine monoxide Cl2 O is a yellow-brown gas that is stable at room temperature. There are two linkage isomers, Cl–Cl–O and Cl–O–Cl, but

Table 17.4.1. Structure of halogen oxides

X2O

a

u

Cl

Cl

a

O O

u a

Cl

O

u u

X2O3

O Br O

b

a

Br O

a a

O

b

– a

O u b

a

O

Cl

O

O

O I

b

a

b

a

b

+

O

Cl O

O

a

O

Cl

O O

b

O

I

O

+

u

a

O

u

X2O5

Br

O Br O

b

a

O

O u

X2O4

X2O7

b

F

XO2

X2O6

a a a

F

b

a X2O2

O

Cl O O O

b

O

a b

a

b

Group 17 and Group 18 Elements only the latter is stable. The stable form Cl–O–Cl is bent (111◦ ) with Cl–O 169 pm. (c) Dibromine monoxide Br2 O is a dark-brown crystalline solid stable at 213 K (mp 255.6 K with decomposition). The molecule has C2v symmetry in both the solid and vapor phases with Br–O 185 pm and angle Br–O–Br 112◦ . (2) X2 O2 molecules Only F2 O2 is known. This is a yellow-orange solid (mp 119 K) that decomposes above 223 K. Its molecular shape resembles that of H2 O2 , although the internal dihedral angel is smaller (87◦ ). The long O–F bond (157.5 pm) and short O–O bond (121.7 pm) in F2 O2 can be rationalized by resonance involving the following valence bond representations: +O

O F–

F

O+

O –F

F

(3) XO2 molecule Only ClO2 is known. Chlorine dioxide is an odd-electron molecule. Theoretical calculations suggest that the odd electron is delocalized throughout the molecule, and this probably accounts for the fact that there is no evidence of dimerization in solution, or even in the liquid or solid phase. Its important Lewis structures are shown below: Cl O

O

O

Cl O

O

Cl

O

(4) X2 O3 molecules (a) Cl2 O3 is a dark-brown solid which explodes even below 273 K. Its structure has not been determined. (b) Br2 O3 is an orange crystalline solid and has been shown by X-ray analysis to be syn-BrOBrO2 with BrI –O 184.5 pm, BrV –O 161.3 pm, and angle Br–O–Br 111.6◦ . It is thus, formally, the anhydride of hypobromous and bromic acid. (5) X2 O4 molecules (a) Chlorine perchlorate, Cl2 O4 , is most likely ClOClO3 . Little is known of the structure and properties of this pale-yellow liquid; it is even less stable than ClO2 and decomposes at room temperature to Cl2 , O2 , and Cl2 O6 . (b) Br2 O4 is a pale yellow crystalline solid, whose structure has been shown by EXAFS to be bromine perbromate, BrOBrO3 , with BrI –O 186.2 pm, BrVII –O 160.5 pm and angle Br–O–Br 110◦ .

663

664

Structural Chemistry of Selected Elements (6) X2 O5 molecules (a) Ozonization of Br2 generates Br2 O3 and eventually Br2 O5 : 3 , 195 K 3 , 195 K Br2 O → Br2O3 O → Br2O5

brown

orange

colorless

The end product can be crystallized from propionitrile as Br2 O5 ·EtCN, and crystal structure analysis has shown that Br2 O5 is O2 BrOBrO2 with each Br atom pyramidally surrounded by three O atoms, and the terminal O atoms are eclipsed with respect to each other. (b) I2 O5 is the most stable oxide of the halogens. Crystal structure analysis has shown that the molecule consists of two pyramidal IO3 groups sharing a common oxygen. The terminal O atoms have a staggered conformation, as shown in Table 17.4.1. (7) X2 O6 molecule − Cl2 O6 is actually a mixed-valence ionic compound ClO+ 2 ClO4 , in which the + − angular ClO2 and tetrahedral ClO4 ions are arranged in a distorted CsCl-type − ◦ crystal structure. Cation ClO+ 2 has Cl–O 141 pm, angle O–Cl–O 119 ; ClO4 has Cl–O(av) 144 pm. (8) X2 O7 molecule Cl2 O7 is a colorless liquid at room temperature. The molecule has C2 symmetry in both gaseous and crystalline states, the ClO3 groups being twisted from the staggered (C2v ) configuration, with Cl–O(bridge) 172.3 pm and Cl–O(terminal) 141.6 pm. In addition to the compounds mentioned above, other unstable binary halogen oxides are known. The structures of the short-lived gaseous XO radicals have been determined. For ClO, the interatomic distance d = 156.9 pm, dipole moment µ = 1.24 D, and bond dissociation energy Do = 264.9 kJ mol−1 . For BrO, d = 172.1 pm, µ = 1.55 D, and Do = 125.8 kJ mol−1 . For IO, d = 186.7 pm and Do = 175 kJ mol−1 . The structures of the less stable oxides I4 O9 and I2 O4 are still unknown, but I4 O9 has been formulated as I3+ (I5+ O3 )3 , and I2 O4 as (IO)+ (IO3 )− . 17.4.2

Ternary halogen oxides

The ternary halogen oxides are mainly compounds in which a heavier X atom (Cl, Br, I) is bonded to both O and F. These compounds are called halogen oxide fluorides. The structures of the ternary halogen oxides are summarized in Fig. 17.4.1. The geometries of these molecules are consistent with the VSEPR model. (a) FClO is bent with Cs symmetry (two lone pairs). (b) FXO2 is pyramidal with Cs symmetry (one lone pair). (c) FXO3 has C3v symmetry. (d) F3 XO is an incomplete trigonal bipyramid with F, O, and a lone pair in the equatorial plane, having Cs symmetry. (e) F3 ClO2 is a trigonal bipyramid with one fluorine and both oxygens in the equatorial plane; owing to the strong repulsion from two

Group 17 and Group 18 Elements F

X

Cl O

F

O

X

F

O

O

171.3

b

X

O

O

F

F

F

a

F

O

Cl

160.5

F

(X = Cl , Br) Cs

(X = Cl , Br, I) C3v

(X = Cl, Br, I) Cs

C2v

(a)

(b)

(c)

(d)

(e)

O F

172.5

F

I

F

F F

181.7

F

O

186.3

O

I

O

184

I

194

F

F

174

O

O

Cl

179

F

O

O

Fig. 17.4.1.

O (X = F, Br, I) Cs (h)

C2h (g)

C4v (f)

140.5

X

F

F

O O

F

Cs

97.2 o

665

Structures of ternary halogen oxides. The bond lengths are in pm. For (c), X = Cl, a = 162 pm, b = 140 pm; X = Br, a = 171 pm, b = 158 pm.

Cl=O double bonds in the equatorial plane, the axial Cl–F bonds are longer than the equatorial Cl–F bonds, as confirmed by experimental data. (f) F5 IO has C4v symmetry, in which the bond lengths are I–Fax 186.3 pm, I–Feq 181.7 pm, and I=O 172.5 pm. Also, the I atom lies above the plane of four equatorial F atoms, and bond angle O–I–Feq is 97.2◦ . (g) F3 IO2 forms oligomeric species, and the dimer (F3 IO2 )2 has C2h symmetry. (h) O3 ClOX are “halogen perchlorate salts”. A variety of cations and anions are derived from some of the above neutral molecules by gaining or losing one F− , as shown in Fig. 17.4.2. Their structures are again in accord with predictions by the VSEPR model.

F

F X

_

O

+

+

X F

O

F

F

Cl O

(a) F2 XO2 –

(b) F2 XO+

(X = Cl, Br, I)

(X = Cl , Br)

C2v

Cs

C2v

F

X

_

F

F

F

(X = Cl, Br, I) C4v

(e) F6 IO– C5v

O I

F

F

(d) F4 XO–

O (c) F2 Cl O2 +

O F

O

F

_

F F

F I=O 176 pm I–F(ax) 182 pm I–F(eq) 188 pm

Fig. 17.4.2.

Structures of cations and anions of ternary halogen oxides.

666

Structural Chemistry of Selected Elements Table 17.4.2. Halogen oxoacids

Generic name

Fluorine

Chlorine

Bromine

Iodine

Hypohalous acids Halous acids Halic acids Perhalic acids

HOF* — — —

HOCl HOClO HOClO2 HOClO3 *

HOBr — HOBrO2 HOBrO3

HOI — HOIO2 * HOIO3 *, (HO)5 IO*

∗

Isolated as pure compounds; others are stable only in aqueous solutions.

17.4.3

Halogen oxoacids and anions

Numerous halogen oxoacids are known, though most of them cannot be isolated as pure species and are stable only in aqueous solution or in the form of their salts. Anhydrous hypofluorous acid (HOF), perchloric acid (HClO4 ), iodic acid (HIO3 ), orthoperiodic acid (H3 IO6 ), and metaperiodic acid (HIO4 ) have been isolated as pure compounds. Table 17.4.2 lists the halogen oxoacids. (1) Hypofluorous and other hypohalous acids At room temperature hypofluorous acid HOF is a gas. Its colorless solid (mp = 156 K) melts to a pale yellow liquid. In the crystal structure, O–F = 144.2 pm, angle H–O–F = 101◦ , and the HOF molecules are linked by O–H· · · O hydrogen bonds (bond length 289.5 pm and bond angle O–H· · · O 163◦ ) to form a planar zigzag chain, as shown below: F

F

F

O

H

O

H

F

O

H

O

O

H

H

F

In general, fluorine has a formal oxidation state of −1, but in HOF and other hypohalous acids HOX, the formal oxidation state of F and X is +1. Hypochlorous acid HOCl is more stable than HOBr and HOI, with Cl–O 169.3 pm and angle H–O–Cl 103◦ in the gas phase. (2) Chlorous acid HOClO and chlorite ion ClO− 2 Chlorous acid, HOClO, is the least stable of the oxoacids of chlorine. It cannot be isolated in pure form, but exists in dilute aqueous solution. Likewise, HOBrO and HOIO are even less stable, showing only a transient existence in aqueous solution. The chlorite ion (ClO− 2 ) in NaClO2 and other salts has a bent structure (C2v symmetry) with Cl–O 156 pm, O–Cl–O 111◦ . –O

Cl

Cl O

O

O–

(3) Halic acids HOXO2 and halate ions XO− 3 Iodic acid, HIO3 , is a stable white solid at room temperature. In the crystal structure, trigonal HIO3 molecules are connected by extensive hydrogen bonding with I–O 181 pm, I–OH 189 pm, angle O–I–O 101◦ , O–I–(OH) 97◦ .

Group 17 and Group 18 Elements

667

Halate ions are trigonal pyramidal, with C3v symmetry, as shown below: X

O

O

–

X = Cl, Cl– O 149 pm X = Br, Br– O 165 pm

O

X = I, I– O 184 pm Angles O–X–O 106º to 107º

Note that in the solid state, some metal halates do not consist of discrete ions. For example, in the iodates there are three short I–O distances 177–90 pm and three longer distances 251–300 pm, leading to distorted pseudo-sixfold coordination and piezoelectric properties. (4) Perchloric acid HClO4 and perhalates XO− 4 Perchloric acid is the only oxoacid of chlorine that can be isolated. The crystal structure of HClO4 at 113 K exhibits three Cl–O distances of 142 pm and a Cl–OH distance of 161 pm. The structure of HClO4 , as determined by electron diffraction in the gas phase, shows Cl–O 141 pm, Cl–OH 163.5 pm, and angles O–Cl–(OH) 106◦ , O–Cl–O 113◦ . The hydrates of perchloric acid exist in at least six crystalline forms. The monohydrate is composed of H3 O+ and ClO− 4 connected by hydrogen bonds. are tetrahedral, with Td symmetry, as shown below: All perhalate ions XO− 4 –

O O

X O

O

X = Cl, Cl–O 144 pm X = Br, Br–O 161 pm X = I, I–O 179 pm

(5) Periodic acids and periodates Several different periodic acids and periodates are known. (a) Metaperiodic acid HIO4 Acid HIO4 consists of one-dimensional infinite chains built up of distorted cisedge-sharing IO6 octahedra, as shown in Fig. 17.4.3. Until now no discrete HIO4 molecule has been found. (b) Orthoperiodic (or paraperiodic) acid (HO)5 IO The crystal structure of orthoperiodic acid, commonly written as H5 IO6 , consists of axially distorted octahedral (HO)5 IO molecules linked into a threedimensional array by O–H · · · O hydrogen bonds (10 for each molecule, I– (OH) 184 pm I– O(bridge) 201 pm I– O(terminal) 191 pm

Fig. 17.4.3.

Structure of metaperiodic aicd.

668

Structural Chemistry of Selected Elements

178 pm

177 pm

Fig. 17.4.4.

Structures of periodates (a) to (d) and hydrogen periodates (e) to (f); small shaded circles represent OH group. 3− (a) IO− 4 in NaIO4 , (b) IO5 in K3 IO5 ,

(a)

(c)

201 pm

(d) 198 pm

pm

I 195 pm

177 pm

I

I

I

(b)

186

4− (c) IO5− 6 in K5 IO6 , (d) I2 O9 in 2− K4 I2 O9 , (e) [IO3 (OH)3 ] in (NH4 )2 IO3 (OH)3 , and (f) [I2 O8 (OH)2 ]4− in K4 [I2 O8 (OH)2 ]·8H2 O.

185 pm

178 pm

95º

O

O

I 200 pm

181 pm

OH

(e)

(f)

260–78 pm). The (HO)5 IO molecule has the maximum number of –OH groups surrounding the I(+7) atom and hence it is called orthoperiodic acid: O HO I OH OH HO OH

I=O 178 pm I– OH 189 pm

The structure of H7 I3 O14 does not show any new type of catenation, because this compound exists in the solid state as a stoichiometric phase containing orthoperiodic and metaperiodic acids according to the formula (HO)5 IO·2HIO4 . The structures of several periodates and hydrogen periodates are shown in Fig. 17.4.4.

17.4.4

Structural features of polycoordinate iodine compounds

Iodine differs in many aspects from the other halogens. Because of the large atomic size and the relatively low ionization energy, it can easily form stable polycoordinate, multivalent compounds. Interest in polyvalent organic iodine compounds arises from several factors: (a) the similarity of the chemical properties and reactivity of I(III) species to those of Hg(+2), Tl(+3), and Pb(+4), but without the toxic and environmental problems of these heavy metal congeners; (b) the recognition of similarities between organic transition-metal complexes and polyvalent main-group compounds such as organoiodine species; and (c) the commercial availability of key precursors, such as PhI(OAc)2 . Six structural types of polyvalent iodine species are commonly encountered, as shown below: L

I+ L L (a)

L

I L

(b)

L L

L I

L +

L (c)

L I L (d)

L L

O L I L L

(e)

L L

L L L L I L L L (f)

Group 17 and Group 18 Elements The first two types, (a) and (b), called iodanes, are conventionally considered as derivatives of trivalent iodine I(+3). The next two, (c) and (d), periodanes, represent the most typical structural types of pentavalent iodine I(+5). The structural types (e) and (f) are typical of heptavalent iodine I(+7). The most important structural features of polyvalent iodine compounds may be summarized as follows: (1) The iodonium ion (type a) generally has a distance of 260–80 pm between iodine and the nearest anion, and may be considered as having pseudotetrahedral geometry about the central iodine atom. (2) Species of type (b) has an approximately T-shaped structure with a collinear arrangement of the most electronegative ligands. Including the nonbonding electron pairs, the geometry about iodine is a distorted trigonal bipyramid with the most electronegative groups occupying the axial positions and the least electronegative group and both electron pairs residing in equatorial positions. (3) The I–C bond lengths in both iodonium salts (type a) and iodoso derivatives (type b) are approximately equal to the sum of the covalent radii of I and C atoms, ranging generally from 200 to 210 pm. (4) For type (b) species with two heteroligands of the same electronegativity, both I–L bonds are longer than the sum of the appropriate covalent radii, but shorter than purely ionic bonds. For example, the I–Cl bond lengths in PhICl2 are 245 pm, whereas the sum of the covalent radii of I and Cl is 232 pm. Also, the I–O bond lengths in PhI(OAc)2 are 215–16 pm, whereas the sum of the covalent radii of I and O is 199 pm. Cl

I

Cl

H3C

C

O

O

C O

I

CH3

O

(5) The geometry of the structural types (c) and (d) can be square pyramidal, pesudo-trigonal bipyramidal, and pesudo-octahedral. The bonding in I(+5) compounds IL5 with a square-pyramidal structure may be described in terms of a normal covalent bond between iodine and the ligand in the apical position, and two orthogonal, hypervalent 3c-4e bonds accommodating four ligands. The carbon ligand and unshared electron pair in this case should occupy the apical positions, with the most electronegative ligands residing at equatorial positions. (6) The typical structures of I(+7) involve a distorted octahedral configuration (type e) about iodine in most periodates and oxyfluoride, IOF5 , and the heptacoordinated, pentagonal bipyramidal species (type f) for the IF7 and IOF− 6 anions. The pentagonal bipyramidal structure can be described as two covalent collinear axial bonds between iodine and ligands in the apical positions and a coplanar, hypervalent 6c-10e bond system for the five equatorial bonds.

669

670

Structural Chemistry of Selected Elements 17.5

Structural chemistry of noble gas compounds

17.5.1

General survey

All the Group 18 elements (He, Ne, Ar, Kr, Xe, and Rn; rare gases or noble gases) have the very stable electronic configurations (1s2 or ns2 np6 ) and are monoatomic gases. The nonpolar, spherical nature of the atoms leads to physical properties that vary regularly with atomic number. The only interatomic interactions are weak van der Waals forces, which increase in magnitude as the polarizabilities of the atoms increase and the ionization energies decrease. In other words, interatomic interactions increase with atomic size. In Section 5.8, we have encountered the noble gas compound HArF and complexes NgMX. The discussion there is mainly concerned with the electronic structures of these linear triatomic species. In recent years, the use of matrixisolation techniques has led to the generation of a wide range of compounds of the general formula HNgY, where Ng = Kr or Xe, and Y is an electronegative atom or group such as H, halides, pseudohalides, OH, SH, C≡CH, and C≡C–C≡CH. These molecules can be easily detected by the extremely strong intensity of the H–Ng stretching vibration. The observed ν(H–Ng) values for some HXeY molecules are Y = H, 1166, 1181; Y = Cl, 1648; Y = Br, 1504; Y = I, 1193; Y = CN, 1623.8, Y = NC, 1851.0 cm−1 . The electronic structure of HNgY is best described in terms of the ion pair HNg+Y− , in which the HNg fragment is held by a covalent bond, and the interaction between Ng and Y is mostly ionic. In this section, we turn our attention to the structural chemistry of those noble gas compounds that can be isolated in bulk quantities. Xenon compounds with direct bonds to the electronegative main-group elements F, O, N, C, and Cl are well established. The first noble gas compound, a yellow-orange solid formulated as XePtF6 , was prepared by Neil Bartlett in 1962. Noting that the first ionization energy of Xe (1170 kJ mol−1 ) is very similar to that of O2 (1175 kJ mol−1 ), and that PtF6 and O2 can combine to form O2 PtF6 , Bartlett replaced O2 by a molar quantity of Xe in the reaction with PtF6 and produced XePtF6 . It is now established that the initial product he obtained was a mixture containing diamagnetic XeII PtIV F6 as the major product, which is most likely a XeF+ salt of (PtF− 5 )n with a polymeric chain structure, as illustrated below, by analogy with the known crystal structure of XeCrF6 . 193 pm Xe

213 pm F Pt

Group 17 and Group 18 Elements

671

O U Ar

Ne

C Fig. 17.5.1.

Structures of CUO(Ne)4−n (Ar)n (n = 0, 1, 2, 3, 4).

If xenon is mixed with a large excess of PtF6 vapor, further reactions proceed as follows: XePtF6 + PtF6 → XeF+ PtF− 6 + PtF5 (non-crystalline)

− ◦ + XeF+ PtF− 6 + PtF5 (warmed ≥ 60 C) → XeF Pt 2 F11 (orange − red solid).

Evidently the Xe(I) oxidation state is not a viable one, and Xe(II) is clearly favored. Until now, no compound of helium has been discovered, and as radon has intense α-radioactivity, information about its chemistry is very limited. Compounds of the other rare gas elements, Ne, Ar, Kr, and Xe, have been reported. For example, experimental investigation of CUO(Ng)n (Ng = Ar, Kr, Xe; n = 1, 2, 3, 4) complexes in solid neon have provided evidence of their formation. The computed structures of CUO(Ne)4−n (Ar)n (n = 0, 1, 2, 3, 4) complexes are illustrated in Fig.17.5.1. 17.5.2

Stereochemistry of xenon

Xenon reacts directly with fluorine to form fluorides. Other compounds of Xe can be prepared by reactions using xenon fluorides as starting materials, which fall into four main types: (1) In combination with F− acceptors, yielding fluorocations of xenon, as in the formation of (XeF5 )(AsF6 ) and (XeF5 )(PtF6 ); (2) In combination with F− donors, yielding fluoroanions of xenon, as in the formation of Cs(XeF7 ) and (NO2 )(XeF8 ); (3) F/H metathesis between XeF2 and an anhydrous acid, such as XeF2 + HOClO3 → F–Xe–OClO3 + HF; (4) Hydrolysis, yielding oxofluorides, oxides, and xenates, such as XeF6 + H2 O → XeOF4 + 2HF. Xenon exhibits a rich variety of stereochemistry. Some of the more important compounds of xenon are listed in Table 17.5.1, and their structures are shown in Fig. 17.5.2. The structural description of these compounds depends on whether

672

Structural Chemistry of Selected Elements Table 17.5.1. Structures of some compounds of xenon with fluorine and oxygen

Compound

Geometry/ symmetry

XeF2

Linear, D∞h

XeO3 XeF+ 3 in (XeF3 )(SbF5 ) XeOF2

Pyramidal, C3v T-shaped, C2v

XeF4

Square planar, D4h Tetrahedral, Td See-saw, C2v

XeO4 XeO2 F2

Xe–O Arrangement in the (pm) bonded and nonbonded electron pairs in Fig. 17.5.2

200 176 184–91

T-shaped, C2v

Square pyramidal, C4v XeO3 F2 Trigonal bipyramidal, D3h XeF+ in Square pyramidal, 5 (XeF5 )(PtF6 ) C4v XeF− Pentagonal planar, 5 in (NMe4 )(XeF5 ) D5h Distorted XeF6 octahedral, C3v Octahedral, Oh XeO4− 6 in K4 XeO6 ·9H2 O XeF− Capped 7 in CsXeF7 octahedral, Cs in Square XeF2− 8 (NO)2 XeF8 antiprismatic, D4d XeOF4

Xe–F (pm)

193

190

174 171

190

170

Trigonal bipyramidal Tetrahedral Trigonal bipyramidal Trigonal bipyramidal Octahedral

(a) (b) (c) (d) (e)

Tetrahedral Trigonal bipyramidal Octahedral

(f) (g)

Trigonal bipyramidal Octahedral

(i)

Pentagonal bipyramidal Capped octahedral

(k)

Octahedral

(m)

193–210

Capped octahedral

(n)

196–208

Square antiprismatic

(o)

179–85 189–203 189(av) 186

(h)

(j)

(l)

only nearest neighbor atoms are considered or whether the electron lone pairs are also taken into consideration. Figure 17.5.2 shows that the known formal oxidation state of xenon ranges from +2 (XeF2 ) to +8 (XeO4 , XeO3 F2 and XeO4− 6 ), and the structures of the xenon compounds are all consistent with the VSEPR model. 17.5.3

Chemical bonding in xenon f luorides

(1) Xenon difluoride and xenon tetrafluoride The XeF2 molecule is linear. A simple bonding description takes the 5pz AO of the xenon atom and the 2pz AO of each fluorine atom to construct the MOs of XeF2 : bonding (σ ), nonbonding (σ n ), and antibonding (σ *), as shown in Fig. 17.5.3. The four valence electrons fill σ and σ n , forming a 3c-4e σ bond extending over the entire F–Xe–F system. Hence the formal bond order of the Xe–F bond can be taken as 0.5. The remaining 5s, 5px and 5py AOs of the Xe

Group 17 and Group 18 Elements

673

Fig. 17.5.2.

Structures of xenon compounds (small shaded circles represent the O atoms): (a) XeF2 , (b) XeO3 , (c) XeF+ 3 , (d) XeOF2 , (e) XeF4 , (f) XeO4 , (g) XeO2 F2 , (h) XeOF4 , (i) XeO3 F2 , ( j) − 4− XeF+ 5 , (k) XeF5 , (l) XeF6 , (m) XeO6 ,

O

F (a)

(b)

(c)

(d)

(e)

2− (n) XeF− 7 , and (o) XeF8 . The electron

(f)

(g)

(h)

(i)

2− lone pairs in XeF− 7 and XeF8 are not shown in the figure. The XeF6 molecule (l) has no static structure but is continually interchanging between eight possible C3v structures in which the lone pair caps a triangular face of the octahedron, but in the figure the lone pair is shown in only one possible position. Also, connecting these C3v structures are the transition states with C2v symmetry in which the lone pair pokes out from an edge of the octahedron.

(j)

a

(k)

(l)

(m)

(n)

(o)

atom are hybridized to form sp2 hybrid orbitals to accommodate the three lone pairs, as shown in Fig. 17.5.2(a). A similar treatment, involving two 3c-4e bonds located in X and Y directions, accounts satisfactorily for the planar structure of XeF4 . The remaining 5s and 5pz AOs of Xe are hybridized to form sp hybrid orbitals that accommodate the two lone-pair electrons, as shown in Fig. 17.5.2(e). The crystal structure of XeF2 is analogous to that of α-KrF2 , which is illustrated in Fig. 17.5.8(a) (see below). –

+

+

–

+ +

–

–

F(2pz)

– –

–

+

Xe(5pz)

+

+

σ*

+

σn

–

σ

F(2pz)

σ*

σn Fig. 17.5.3.

σ

Xe

XeF2

2F

(2) Xenon hexafluoride There are two possible theoretical models for the isolated XeF6 molecule: (i) regular octahedral (Oh symmetry), with three 3c-4e bonds and a sterically inactive lone pair of electrons occupying a spherically symmetric s orbital, or (ii) distorted octahedral (C3v symmetry), where the lone pair is sterically active and lies above the center of one face, but the molecule is readily converted into other configurations. All known experimental data are consistent with the

Molecular orbitals of the 3c-4e F–Xe–F σ bond of XeF2 : (a) the possible combinations of the AOs of Xe and F atoms, and (b) the schematic energy levels of XeF2 molecule.

674

Structural Chemistry of Selected Elements following nonrigid model. Starting from the C3v structure, the electron pair can move across an edge between two F atoms (C2v symmetry for the intermediate configuration) to an equivalent position surrounded by three F atoms. This continuous molecular rearrangement, designated as a C3v → C2v → C3v transformation, involves only modest changes in bond angles and virtually no change in bond lengths. (3)

− Perfluoroxenates XeF2− 8 and XeF7

There are nine electron pairs in XeF2− 8 , which are to be accommodated around the Xe atom. From experimental data, the XeF2− 8 ion has a square antiprismatic structure [Fig. 17.5.2(o)] showing no distortion that could reveal a possible position for the nonbonding pair of electrons. The lone pair presumably resides in the spherical 5s orbital. There are eight electron pairs to be placed around the Xe atom in XeF− 7 . Six F atoms are arranged octahedrally around the central Xe atom. The approach of the seventh F atom [labelled “a” for this F atom in Fig. 17.5.2(n)] towards the midpoint of one of the faces causes severe distortion of the basic octahedral shape. Such a distortion could easily mask similar effects arising from a nonspherical, sterically active lone pair. The bond between Xe atom and the capping fluorine atom F(a) has the length Xe–F(a) 210 pm, or about 17 pm longer than the other Xe–F bonds, which might suggest some influence of a lone pair in the F(a) direction. 17.5.4

Structures of some inorganic xenon compounds

The structure and bonding of the [AuXe4 ]2+ cation in (AuXe4 )(Sb2 F11 )2 have been discussed in Section 2.4.3. Some other interesting inorganic xenon compounds are described below. (1) Xe2 Sb4 F21 Although the Xe+ 2 cation is known to exist from Raman spectroscopy, with ν(Xe–Xe) = 123 cm−1 , its bond length was only determined in 1997 from the crystal structure of Xe2 Sb4 F21 . The Xe–Xe bond length is 309 pm, the longest recorded homonuclear bond between main-group elements. (2) Complexes of xenon fluorides The pentafluoride molecules, such as AsF5 and RuF5 , act essentially as fluoride ion acceptors, so that their complexes with xenon fluorides can be formulated as salts containing cationic xenon species, e.g., [XeF][AsF6 ], [XeF][RuF6 ], [Xe2 F3 ][AsF6 ], [XeF3 ][Sb2 F11 ], and [XeF5 ][AgF4 ]. In a number of adducts of XeF2 with metal complexes, the configuration at the Xe atom remains virtually linear, with one F atom lying in the coordination sphere of the metal atom. The ion Xe–F+ does not ordinarily occur as a discrete ion, but rather is attached covalently to a fluorine atom on the anion. Figure 17.5.4(a) shows the structure of [XeF][RuF6 ]. The terminal Xe–F(t) bond is appreciably shorter than that in XeF2 (200 pm), while the bridging Xe–F(b) bond is longer. Table 17.5.2 lists the Xe–F bond lengths in some adducts of this type.

Group 17 and Group 18 Elements (a)

675

(b) 251 pm

187.2 pm Xe

235 pm

218.2 pm

Ni 221 pm

Ru

Xe

F

Fig. 17.5.4.

F

Structure of (a) [XeF][RuF6 ] and (b) [Xe2 F11 ]2 [NiF6 ].

In the crystal structure of [XeF3 ][Sb2 F11 ], the T-shaped XeF+ 3 cation is nearly group in a close Xe· · · F contact, as shown coplanar with a F atom of a Sb2 F− 11 below. The terminal Sb–F bond lengths of the anion lie in the range 183–9 pm. 183 188 Xe 189

204

250 pm

F

201 190 Sb

The crystal structure of [XeF5 ][AgF4 ] consists of alternate stacks of double layers of square-pyramidal XeF+ 5 cations and approximately square-planar anions (site symmetry D , Ag–F = 190.2 pm). The XeF+ AgF− 2h 5 ion has C4v 4 symmetry with Xe–F(ax) = 185.2, Xe–F(eq) = 182.6 pm, and F(ax)–Xe– F(eq) = 77.7◦ . Each cation lying on a 4-axis interacts with one bridging F ligand of each of four anions at 263.7 pm, as illustrated below: F(ax) F(eq) Xe

Table 17.5.2. Xe–F bond lengths in some complexes containing XeF+

Compound

Xe–F(t) (pm)

Xe–F(b) (pm)

F–Xe–FAsF5 F–Xe–FRuF5 F–Xe–FWOF4 F–Xe–Sb2 F10

187 187 189 184

214 218 204 235

676

Structural Chemistry of Selected Elements The [Xe2 F3 ]+ cation in [Xe2 F3 ][AsF6 ] is V-shaped, as shown below: F 180˚

Xe

151˚

214 pm Xe

190 pm

F

F

The [Xe2 F11 ]+ cation can be considered as [F5 Xe · · · F · · · XeF5 ]+ by ana2− + − logy to [Xe2 F3 ]+ . The compounds [Xe2 F+ 11 ]2 [NiF6 ] and [Xe2 F11 ] [AuF6 ] contain Ni(IV) and Au(V), respectively. Figure 17.5.4(b) shows the structure of [Xe2 F11 ]2 [NiF6 ]. (3) FXeOSO2 F When XeF2 reacts with an anhydrous acid, such as HOSO2 F, elimination of HF occurs to yield FXeOSO2 F, which contains a linear F–Xe–O group, as shown in Fig. 17.5.5(a). (4) FXeN(SO2 F)2 This compound is produced by the replacement of a F atom in XeF2 by a N(SO2 F)2 group from HN(SO2 F)2 . Its molecular structure has a linear F–Xe–N fragment and a planar configuration at the N atom, as shown in Fig. 17.5.5(b). (5) Cs2 (XeO3 Cl2 ) This salt is obtained from the reaction of XeO3 with CsCl in aqueous HCl solution, and contains an anionic infinite chain. Figure 17.5.5(c) shows the structure of the chain [Xe2 O6 Cl4 ]4n− n . (6) M(CO)5 E (M = Cr, Mo, W; E = Ar (W only), Kr, Xe) These complexes are transient species generated from photolysis of M(CO)6 in supercritical noble gas solution at room temperature. Their octahedral structure (symmetry C4v ) has been characterized by IR spectroscopy and solution NMR. The noble gas atom E can be formally considered as a neutral two-electron donor ligand, and the bonding involves interactions between the p orbitals of E and orbitals on the equatorial CO groups. The stabilities of the complexes decrease in the order W > Mo ∼ Cr and Xe > Kr > Ar. Organometallic noble gas complexes F

177.5˚

O

216 pm

4n–

178.1º

194 pm

197 pm

Xe O

N

220 pm

Xe

S S

Xe

Cl O

n

Fig. 17.5.5.

Structures of some inorganic xenon compounds: (a) FXeOSO2 F, (b) FXeN(SO2 F)2 , and (c) [Xe2 O6 Cl4 ]4n− n .

Group 17 and Group 18 Elements

677

that can be generated using matrix isolation techniques include Fe(CO)4 Xe, Rh(η5 -C5 R5 )(CO)E (R = H, Me; E = Kr, Xe), M(η5 -C5 R5 )(CO)2 E (M = Mn, Re; R = H, Me, Et (Mn only); E = Ar (only with Re and C5 H5 ), Kr, Xe), and M(η5 -C5 H5 )(CO)3 Xe (M = Nb, Ta). 17.5.5

Structures of some organoxenon compounds

More than ten organoxenon compounds which contain Xe–C bonds have been prepared and characterized. The first structural characterization of a Xe–C bond was performed on [MeCN–Xe–C6 H5 ]+ [(C6 H5 )2 BF2 ]− · MeCN. The structure of the cation [MeCN–Xe–C6 H5 ]+ is shown in Fig. 2.4.4. The Xe–C bond length is 209.2 pm, and the Xe–N bond length is 268.1 pm, with the Xe atom in a linear environment. This compound has no significant fluorine bridge between cation and anion, as the shortest intermolecular Xe · · · F distance is 313.5 pm. Other examples of compounds containing Xe–C bonds are shown in Fig. 17.5.6 and described below.

(1) Xe(C6 F5 )2 This is the first reported homoleptic organoxenon(II) compound with two Xe–C bonds of length 239 and 235 pm, longer than the corresponding bond in other compounds by about 30 pm. The C–Xe–C unit is almost linear (angle 178◦ ) and the two C6 F5 rings are twisted by 72.5◦ with respect to each other. (2) [(C6 F5 Xe)2 Cl][AsF6 ] This is the first isolated and unambiguously characterized xenon(II) chlorine compound. The cation [(C6 F5 Xe)2 Cl]+ consists of two C6 F5 Xe fragments bridged through a chloride ion. Each linear C–Xe–Cl linkage can be considered to involve an asymmetric hypervalent 3c-4e bond. Thus a shorter Xe–C distance (mean value 211.3 pm) occurs and is accompanied by a longer Xe–Cl distance (mean value 281.6 pm). The Xe–Cl–Xe angle is 117◦ . (a)

(b)

239 pm

278.4 pm 211.6 pm

Cl

284.7 pm 211.1 pm

Xe

235 pm Xe

(c)

(d) Fig. 17.5.6. 209 pm

209 pm

269.5 pm N Xe F

279 pm Xe

H

F B

Structures of some organoxenon compounds: (a) Xe(C6 F5 )2 , (b) the cation [(C6 F5 Xe)2 Cl]+ , (c) the cation (2,6-F2 H3 C5 N–Xe–C6 F5 )+ , and (d) 2,6-F2 H3 C6 –Xe–FBF3 .

678

Structural Chemistry of Selected Elements (3) [2,6-F2 H3 C5 N–Xe–C6 F5 ][AsF6 ] In the structure of the cation (2,6-F2 H3 C5 N–Xe–C6 F5 )+ , the Xe atom is (exactly) linearly bonded to C and N atoms; the bond lengths are Xe–C 208.7 pm and Xe–N 269.5 pm. (4) 2,6-F2 H3 C6 –Xe–FBF3 In this compound the Xe atom is linearly bonded to C and F atoms; bond lengths are Xe–C 209.0 pm and Xe–F 279.36 pm and the bond angle C–Xe–F is 167.8◦ . The structural data of three other organoxenon compounds are listed below: Compound (C6 F5 –Xe)(AsF6 ) O || (C6 F5 –Xe)(OCC6 F5 ) (F2 H3 C6 –Xe)(OSO2 CF3 )

Xe–C (pm)

Xe–E (pm)

C–Xe–E

(1) 207.9

271.4

170.5◦

(2) 208.2

267.2

174.2◦

212.2 (1) 207.4 (2) 209.2

236.7 268.7 282.9

178.1◦ 173.0◦ 165.1◦

In the known organoxenon compounds, the C–Xe–E angle (E = F, O, N, Cl) deviates only slightly from 180◦ , indicating a hypervalent 3c-4e bond in all cases. The Xe–C bond lengths, except in the compound Xe(C6 F5 )2 , vary within the range 208–12 pm. All Xe· · · E contacts are significantly shorter than the sum of the van der Waals radii of Xe and E, indicating at least a weak secondary Xe· · · E interaction. 17.5.6

Gold–xenon complexes

Xenon can act as a complex ligand to form M–Xe bonds, especially with gold, which exhibits significant relativistic effects in view of its electronic structure, as discussed in Section 2.4.3. Some gold–xenon complexes have been prepared and characterized, and their structures are shown in Fig. 17.5.7. − The compound [AuXe2+ 4 ][Sb2 F11 ]2 is mentioned in Section 2.4.3 in the context of relativistic effects. In fact it exists in two crystallographically distinct modifications: triclinic and tetragonal. The cation [AuXe4 ]2+ is square planar with Au–Xe bond lengths ranging from 267.0 to 277.8 pm (Fig. 17.5.7(a)). Around the gold atom, there are three weak Au· · · F contacts of 267.1 to 315.3 pm for the triclinic modification, and two contacts of Au· · · F 292.8 pm for the tetragonal modification. Figures 17.5.7(b) and (c) compare the structure of trans-[AuXe2 ][SbF6 ]2 with that of the trans-[AuXe2 F][SbF6 ] moiety in crystalline [AuXe2 F][SbF6 ] [Sb2 F11 ]. Each Au atom resides in a square-planar environment, with two Xe atoms and two F atoms bonded to it. The Au–Xe bond length is 270.9 pm for the former and 259.3 to 261.9 pm for the latter. Figure 17.5.7(d) shows the structure of [AuXe2 ][Sb2 F11 ]2 . The Au–Xe distances of 265.8 and 267.1 pm are slightly shorter than those in the [AuXe4 ]2+ ion.

Group 17 and Group 18 Elements (a)

(b)

679

(c)

Sb Au

F

Xe

(d)

(e)

Fig. 17.5.7.

Structures of some gold–xenon complexes: (a) [AuXe4 ]2+ , (b) AuXe2 (SbF6 )2 , (c) (AuXe2 F)(SbF6 ), (d) (AuXe2 )(Sb2 F11 )2 , and (e) (Au2 Xe2 F)3+ and its immediate anion environment in [Au2 Xe2 F][SbF6 ]3 .

Figure 17.5.7(e) shows the structure of the Z-shaped binuclear [Xe–Au–F– Au–Xe]3+ ion and its immediate anion environment in [Au2 Xe2 F][SbF6 ]3 . The Au atom is coordinated by one Xe atom and three F atoms in a square-planar configuration, with Au–Xe bond length 264.7 pm. 17.5.7

Krypton compounds

The known compounds of krypton are limited to the +2 oxidation state, and the list includes the following: (a) KrF2 (b) Salts of KrF+ and Kr2 F+ 3: [KrF][MF6 ] (M = P, As, Sb, Bi, Au, Pt, Ta, Ru) [KrF][M2 F11 ] (M = Sb, Ta, Nb) [Kr2 F3 ][MF6 ] (M = As, Sb, Ta) [KrF][AsF6 ]·[Kr2 F3 ][AsF6 ] (c) Molecular adducts: KrF2 ·MOF4 (M = Cr, Mo, W) KrF2 · nMoOF (n = 2, 3) KrF2 ·VF5 KrF2 ·MnF4 KrF2 ·[Kr2 F3 ][SbF5 ]2 KrF2 ·[Kr2 F3 ][SbF6 ] (d) Other types salts of [RCN–KrF]+ (R = H, CF3 , C2 F5 , nC3 F7 ) Kr(OTeF5 )2 (1) Structure of KrF2 Krypton difluoride KrF2 exists in two forms in the solid state: α-KrF2 and βKrF2 , whose crystal structures are shown in Fig. 17.5.8. Specifically, α-KrF2

680

Structural Chemistry of Selected Elements (a)

(b)

271 pm 189.4 pm

189 pm

271 pm

Kr Fig. 17.5.8.

Crystal structure of (a) α-KrF2 and (b) β-KrF2 .

F

crystallizes in a body-centered tetragonal lattice, with space group I 4/mmm, and all the KrF2 molecules are aligned parallel to the c axis. In contrast, βKrF2 belongs to tetragonal space group P42 /mnm, in which the KrF2 molecules located at the corners of the unit cell all lie in the ab plane and are rotated by 45◦ with respect to the a axis. The central KrF2 molecule also lies in the ab plane, but its molecular axis is orientated perpendicular to those of the corner KrF2 molecules. The Kr–F bond length in α-KrF2 is 189.4 pm and is in excellent agreement with those determined for β-KrF2 , 189 pm, by X-ray diffraction and for gaseous KrF2 by electron diffraction, 188.9 pm. The interatomic F· · · F distance between collinearly orientated KrF2 molecules is 271 pm in both structures.

M

F Kr

M = As, Sb, Bi Fig. 17.5.9.

Structure of [KrF][MF6 ] (M = AS, Sb, Bi).

(2) Structures of [KrF][MF6 ] (M = As, Sb, Bi) These three compounds form an isomorphous series, in which the [KrF]+ cation strongly interacts with the anion by forming a fluorine bridge with the pseudo-octahedral anion bent about Fb , as shown in Fig. 17.5.9. The terminal Kr–Ft bond lengths in these salts (176.5 pm for [KrF][AsF6 ] and [KrF][SbF6 ], 177.4 pm for [KrF][BiF6 ]) are shorter, and the Kr–Fb bridge bond lengths (213.1 pm for [KrF][AsF6 ], 214.0 pm for [KrF][SbF6 ], and 209.0 pm for [KrF][BiF6 ]) are longer, than the Kr–F bonds of α-KrF2 (189.4 pm). The Kr–Fb –M bridge bond angles (133.7◦ for [KrF][AsF6 ], 139.2◦ for [KrF][SbF6 ], and 138.3◦ for [KrF][BiF6 ]) are consistent with the bent geometry predicted by the VSEPR arrangements at their respective Fb atoms, but are more open than the ideal tetrahedral angle.

References 1. N. N. Greenwood and A. Earnshaw, Chemistry of the Elements, 2nd edn., Butterworth-Heinemann, Oxford, 1997. 2. A. G. Massey, Main Group Chemistry, 2nd edn., Wiley, Chichester, 2000.

Group 17 and Group 18 Elements 3. C. E. Housecroft and A. G. Sharpe, Inorganic Chemistry, 2nd edn., Prentice-Hall, Harlow, 2004. 4. D. F. Shriver, P. W. Atkins, T. L. Overton, J. P. Rourke, M. T. Weller and F. A. Armstrong, Inorganic Chemistry, 4th edn., Oxford University Press, Oxford, 2006. 5. G. Meyer, D. Naumann and L. Wesemann (eds.), Inorganic Chemistry Highlights, Wiley–VCH, Weimheim, 2002. 6. M. Pettersson, L. Khriachtchev, J. Lundell and M. Räsänen, Noble gas hydride compounds. In G. Meyer, D. Naumann and L. Wesemann (eds.), Inorganic Chemistry in Focus II, Wiley–VCH,Weinheim, 2005, pp. 15–34. 7. N. Bartlett (ed.), The Oxidation of Oxygen and Related Chemistry: Selected Papers of Neil Bartlett, World Scientific, Singapore, 2001. 8. K. Akiba (ed.), Chemistry of Hypervalent Compounds, Wiley–VCH, New York, 1999. 9. A. J. Blake, F. A. Devillanova, R. O. Gould, W.-S. Li, V. Lippolis, S. Parsons, C. Radek and M. Schröder, Template self-assembly of polyiodide networks. Chem. Soc. Rev. 27, 195–205 (1998). 10. J. Li, S. Irle, and W. H. E. Schwarz, Electronic structure and properties of trihalogen + X+ 3 and XY2 . Inorg. Chem. 35, 100–9 (1996). 11. D. B. Morse, T. B. Rauchfuss and S. R. Wilson, Main-group-organotransition metal chemistry: the cyclopentadienylchromium polyiodides including 2− [(C5 Me5 )2 Cr2 I+ 3 ]2 [I16 ]. J. Am. Chem. Soc. 112, 1860–4 (1990). 12. T. Kraft and M. Jansen, Crystal structure determination of metaperiodic acid, HIO4 , with combined X-ray and neutron diffraction. Angew. Chem. Int. Ed. 36,1753–4 (1997). 13. M. Jansen and T. Kraft, The structural chemistry of binary halogen oxides in the solid state. Chem. Ber, 130, 307–15 (1997). 14. J. H. Holloway and E. G. Hope, Recent advances in noble-gas chemistry. Adv. Inorg. Chem. 46, 51–100 (1999). 15. T. Drews and K. Seppelt, The Xe+ 2 ion – preparation and structure. Angew. Chem. Int. Ed. 36, 273–4 (1997). 16. O. S. Jina, X. Z. Sun and M. W. George, Do early and late transition metal noble gas complexes react by different mechanisms? A room temperature time-resolved infrared study of (η5 -C5 H5 )Rh(CO)2 (R = H or Me) in supercritical noble gas solution at room temperature. Dalton Trans., 1773–8 (2003). 17. H. Bock, D. Hinz-Hübner, U. Ruschewitz and D. Naumann, Structure of bis(pentafluorophenyl)xenon, Xe(C6 F5 )2 . Angew. Chem. Int. Ed. 41, 448–50 (2002). 18. J. F. Lehmann, D. A. Dixon and G. J. Schrobilgen, X-ray crystal structures of α-KrF2 , [KrF][MF6 ] (M = As, Sb, Bi), [Kr2 F3 ][SbF6 ]·KrF2 , [Kr2 F3 ]2 [SbF6 ]2 ·KrF2 , and [Kr2 F3 ][AsF6 ]·[KrF][AsF6]; Synthesis and characterization of [Kr2 F3 ][PF6 ]·nKrF2 ; and theoretical studies of KrF2 , KrF+ , Kr2 F+ 3, and the [KrF][MF6 ] (M = P, As, Sb, Bi) ion pairs. Inorg. Chem. 40, 3002–17 (2001). 19. T. Drews, S. Seidal and K. Seppelt, Gold–xenon complexes. Angew. Chem. Int. Ed. 41, 454–6 (2002). 20. B. Liang, L, Andrews, J. Li and B. E. Bursten, On the noble-gas-induced intersystem crossing for the CUO molecule. Inorg. Chem. 43, 882–94 (2004).

681

18

Structural Chemistry of Rare-Earth Elements

18.1

Chemistry of rare-earth metals

The lanthanides (Ln) include lanthanum (La) and the following fourteen elements—Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb and Lu— in which the 4f orbitals are progressively filled. These fifteen elements together with scandium (Sc) and yttrium (Y) are termed the rare-earth metals. The designation of rare earths arises from the fact that these elements were first found in rare minerals and were isolated as oxides (called earths in the early literature). In fact, their occurrence in nature is quite abundant, especially in China, as reserves have been estimated to exceed 84 ×106 tons. In a broader sense, even the actinides (the 5f elements) are sometimes included in the rare-earth family. The rare-earth metals are of rapidly growing importance, and their availability at quite inexpensive prices facilitates their use in chemistry and other applications. Much recent progress has been achieved in the coordination chemistry of rare-earth metals, in the use of lanthanide-based reagents or catalysts, and in the preparation and study of new materials. Some of the important properties of rare-earth metals are summarized in Table 18.1.1. In this table, rM is the atomic radius in the metallic state and rM3+ is the radius of the lanthanide(III) ion in an eight-coordinate environment. 18.1.1

Trends in metallic and ionic radii: lanthanide contraction

The term lanthanide contraction refers to the phenomenon of a steady decrease in the radii of the Ln3+ ions with increasing atomic number, from La3+ to Lu3+ , amounting overall to 18 pm (Table 18.1.1). A similar contraction occurs for the metallic radii and is reflected in many smooth and systematic changes, but there are marked breaks at Eu and Yb. Lanthanide contraction arises because the 4f orbitals lying inside the 4d, 5s, and 5p orbitals provide only incomplete shielding of the outer electrons from the steadily increasing nuclear charge. Therefore the outer electron cloud as a whole steadily shrinks as the 4f subshell is filled. In recent years, theoretical work suggests that relativistic effects also plays a significant role. Further details are given in Section 2.4.3. The spectacular irregularity in the metallic radii of Eu and Yb occurs because they have only two valence electrons in the conduction band, whereas the other lanthanide metals have three valence electrons in the 5d/6s conduction band. Therefore, lanthanide contraction is not manifested by Eu and Yb in the metallic

Rare-Earth Elements

683

Table 18.1.1. Properties of the rare-earth metals

Symbol name

Sc Y La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

Scandium Yttrium Lanthanum Cerium Praseodymium Neodymium Promethium Samarium Europium Gadolinium Terbium Dysprosium Holmium Erbium Thulium Ytterbium Lutetium

Electronic configuration Metal

M3+

rM (pm) (CN = 12)

rM3+ (pm) (CN = 8)

[Ar]3d1 4s2 [Kr]4d1 5s2 [Xe]5d1 6s2 [Xe]4f1 5d1 6s2 [Xe]4f3 6s2 [Xe]4f4 6s2 [Xe]4f5 6s2 [Xe]4f6 6s2 [Xe]4f7 6s2 [Xe]4f7 5d1 6s2 [Xe]4f9 6s2 [Xe]4f10 6s2 [Xe]4f11 6s2 [Xe]4f12 6s2 [Xe]4f13 6s2 [Xe]4f14 6s2 [Xe]4f14 5d1 6s2

[Ar] [Kr] [Xe] [Xe]4f1 [Xe]4f2 [Xe]4f3 [Xe]4f4 [Xe]4f5 [Xe]4f6 [Xe]4f7 [Xe]4f8 [Xe]4f9 [Xe]4f10 [Xe]4f11 [Xe]4f12 [Xe]4f13 [Xe]4f14

164.1 180.1 187.9 182.5 182.8 182.1 (181.0) 180.4 204.2 180.1 178.3 177.4 176.6 175.7 174.6 193.9 173.5

87.1 101.9 116.0 114.3 112.6 110.9 (109.5) 107.9 106.6 105.3 104.0 102.7 101.5 100.4 99.4 98.5 97.7

state or in some compounds such as the hexaborides, where the lower valence of these two elements is evident from the large radii compared with those of neighboring elements. Lanthanide contraction has important consequences for the chemistry of the third-row transition metals. The reduction in radius caused by the poor shielding ability of the 4f electrons means that the third-row transition metals are approximately the same size as their second-row congeners, and consequently exhibit similar chemical behavior. For instance, it has been shown that the covalent radius of gold (125 pm) is less than that of silver (133 pm).

18.1.2

Crystal structures of the rare-earth metals

The 17 rare-earth metals are known to adopt five crystalline forms. At room temperature, nine exist in the hexagonal closest packed structure, four in the double c-axis hcp (dhcp) structure, two in the cubic closest packed structure and one in each of the body-centered cubic packed and rhombic (Sm-type) structures, as listed in Table 18.1.1. This distribution changes with temperature and pressure as many of the elements go through a number of structural phase transitions. All of the crystal structures, with the exception of bcp, are closest packed, which can be defined by the stacking sequence of the layers of closepacked atoms, and are labeled in Fig. 18.1.1. hcp: AB· · · ccp: ABC· · ·

dhcp: ABAC· · · Sm-type: ABABCBCAC· · ·

Crystal structure hcp hcp dhcp ccp dhcp dhcp dhcp rhom bcp hcp hcp hcp hcp hcp hcp ccp hcp

Lattice parameters a (pm)

c (pm)

330.9 364.8 377.4 516.1 367.2 365.8 365.0 362.9 458.3 363.4 360.6 359.2 357.8 355.9 353.8 548.5 350.5

526.8 573.2 1217.1 — 1183.3 1179.7 1165 2620.7 — 578.1 569.7 565.0 561.8 558.5 555.4 — 554.9

684

Structural Chemistry of Selected Elements A

A

B

B A

A

B

C

A

A

hcp

Fig. 18.1.1.

ccp

Structure types of rare-earth metals.

A B C B

dhcp A

C

B

A

C

C

A

A bcp

Sm-type

If Ce, Eu, and Yb are excluded, then the remaining 14 rare-earth metals can be divided into two major subgroups: (a) The heavy rare-earth metals Gd to Lu, with the exception of Yb and the addition of Sc and Y—these metals adopt the hcp structure. (b) The light rare-earth metals La to Sm, with the exception of Ce and Eu— these metals adopt the dhcp structure. (The Sm-type structure can be viewed as a mixture of one part of ccp and two parts of hcp.) Within each group, the chemical properties of the elements are very similar, so that they invariably occur together in mineral deposits. 18.1.3

Oxidation states

Because of stability of the half-filled and filled 4f subshell, the electronic configuration of the Ln atom is either [Xe]4f n 5d0 6s2 or [Xe]4f n 5d1 6s2 . The most stable and common oxidation state of Ln is +3. The principal reason is that the fourth ionization energy I4 of a rare-earth atom is greater than the sum of the first three ionization energies (I1 + I2 + I3 ), as listed in Table 18.1.2. The energy required to remove the fourth electron is so great that in most cases it cannot be compensated by chemical bond formation, and thus the +4 oxidation state rarely occurs. Although the +3 oxidation state dominates lanthanide chemistry, other oxidation states are accessible, especially if a 4f0 , 4f7 or 4f14 configuration is generated. The most common 2+ ions are Eu2+ (4f7 ) and Yb2+ (4f14 ), and the most common 4+ ions are Ce4+ (4f0 ) and Tb4+ (4f7 ). Of the five lanthanides that exhibit tetravalent chemistry, Nd4+ and Dy4+ are confined to solid-state

Rare-Earth Elements Table 18.1.2. Ionization energies of rare-earth elements (kJ mol−1 )

Element

I1

I2

I3

Sc Y La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

633 616 538 527 523 530 536 543 547 593 565 572 581 589 597 603 524

1235 1181 1067 1047 1018 1035 1052 1068 1085 1167 1112 1126 1139 1151 1163 1176 1340

2389 1980 1850 1949 2086 2130 2150 2260 2404 1990 2114 2200 2204 2194 2285 2415 2022

(I1 + I2 + I3 ) 4257 3777 3455 3523 3627 3695 3738 3871 4036 3750 3791 3898 3924 3934 4045 4194 3886

I4 7091 5963 4819 3547 3761 3899 3970 3990 4110 4250 3839 4001 4100 4115 4119 4220 4360

fluoride complexes, while Pr4+ (4f1 ) and Tb4+ also form the tetrafluoride and dioxide. The most extensive lanthanide(IV) chemistry is that of Ce4+ , for which a variety of tetravalent compounds and salts are known (e.g., CeO2 , CeF4 ·H2 O). The common occurrence of Ce4+ is attributable to the high energy of the 4f orbitals at the start of the lanthanide series, such that Ce3+ is not sufficiently stable to prevent the loss of an electron. The crystallographic ionic radii of the rare-earth elements in oxidation states +2 (CN = 6), +3 (CN = 6), and +4 (CN = 6) are presented in Table 18.1.3. The data provide a set of conventional size parameters for the calculation of hydration energies. It should be noted that in most lanthanide(III) complexes the Ln3+ center is surrounded by eight or more ligands, and that in aqueous solution the primary coordination sphere has eight and nine aqua ligands for light and heavy Ln3+ ions, respectively. The crystal radii of Ln3+ ions with CN = 8 are listed in Table 18.1.1. 18.1.4

Term symbols and electronic spectroscopy

Atomic and ionic energy levels are characterized by a term symbol of the general form 2S+1 LJ . The values of S, L, and J of lanthanide ions Ln3+ in the ground state can be deduced from the arrangement of the electrons in the 4f subshell, which are determined by Hund’s rules and listed in Table 18.1.4. Three types of electronic transition can occur for lanthanide compounds. These are f→f transition, nf → (n + 1)d transition and ligand → metal f charge-transfer transition. In Ln3+ ions, the 4f orbitals are radially much more contracted than the d orbitals of transition metals, to the extent that the filled 5s and 5p orbitals largely shield the 4f electrons from the ligands. The result is that vibronic coupling is much weaker in Ln3+ compounds than in transition-metal compounds, and hence the intensities of electronic transitions are much lower. As many of

685

686

Structural Chemistry of Selected Elements Table 18.1.3. Crystallographic ionic radii (pm) and hydration entropies (kJ mol−1 ) of the rare-

earth elements in oxidation states +2, +3 and +4 Element

rM2+ (CN = 6)

−'hyd H ◦ (M2+ )

rM3+ (CN = 6)

−'hyd H ◦ (M3+ )

rM4+ (CN = 8)

— — 130.4 127.8 125.3 122.5 120.6 118.3 116.6 114.0 111.9 109.6 107.5 105.6 103.8 102.6 —

— — — — 1438 1459 1474 1493 1507 — 1546 1566 1585 1602 1619 1631 —

74.5 90.0 103.2 101.0 99.0 98.3 97.0 95.8 94.7 93.8 92.1 91.2 90.1 89.0 88.0 86.8 86.1

— 3640 3372 3420 3453 3484 3520 3544 3575 3597 3631 3661 3692 3718 3742 3764 3777

— — — 96.7 94.9 93.6 92.5 91.2 90.3 89.4 88.6 87.4 86.4 85.4 84.4 83.5 82.7

Sc Y La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

−'hyd H ◦ (M4+ ) — — — 6390 6469 6528 6579 6639 6682 6726 6765 6824 6875 6926 6978 7026 7069

these electronic transitions lie in the visible region of the electromagnetic spectrum, the colors of Ln3+ compounds are typically less intense than those of the transition metals. The colors of the Ln3+ ions in hydrated salts are given in Table 18.1.4. The lack of 4f orbital and ligand interaction means that the f→f Table 18.1.4. Electronic configuration, ground state term symbol, and magnetic properties of Ln3+ ions

Ln3+

La3+ Ce3+ Pr3+ Nd3+ Pm3+ Sm3+ Eu3+ Gd3+ Tb3+ Dy3+ Ho3+ Er3+ Tm3+ Yb3+ Lu3+

4f electronic Ground state configuration term symbol

4f 0 4f1 4f2 4f 3 4f 4 4f 5 4f6 4f7 4f8 4f 9 4f10 4f 11 4f12 4f 13 4f14

1S 0 2F 5/2 3H 4 3I 9/2 5I 4 6H 5/2 7F 0 8S 7/2 7F 6 6H 15/2 5I 8 4I 15/2 3H 6 2F 7/2 1S 0

Color of Ln3+

Colorless Colorless Green Lilac Pink Pale yellow Colorless Colorless Very pale pink Pale yellow Yellow Pink Pale green Colorless Colorless

Magnetic moment, µ(298 K)/µB Calculated

Observed

0 2.54 3.58 3.62 2.68 0.85 0 7.94 9.72 10.65 10.60 9.58 7.56 4.54 0

0 2.3–2.5 3.4–3.6 3.5–3.6 2.7 1.5–1.6 3.4–3.6 7.8–8.0 9.4–9.6 10.4–10.5 10.3–10.5 9.4–9.6 7.1–7.4 4.4–4.9 0

transition energies for a given Ln3+ change little between compounds, and hence the colors of Ln3+ are often characteristic. In view of the small interaction

Rare-Earth Elements of the Ln3+ 4f orbitals with the surrounding ligands, the f→f transition energies in Ln3+ compounds are well defined, and thus the bands in their electronic absorption spectra are much sharper. Since f→d transitions are Laporte allowed, they have much higher intensity than f→f transitions. Ligand-to-metal charge-transfer transitions are also Laporte allowed and also have high intensity. These two types of transitions generally fall in the ultraviolet region, so they do not affect the colors of Ln3+ compounds. For easily reduced Ln3+ (Eu and Yb), they are at lower energy than the f→d transitions, and for easily oxidized ligands they may tail into the visible region of the spectrum, giving rise to much more intensely colored complexes. The Ln2+ ions are often highly colored. This arises because the 4f orbitals in Ln2+ are destabilized with respect to those in Ln3+ , and hence lie closer in energy to the 5d orbitals. This change in orbital energy separation causes the f→d transitions to shift from the ultraviolet into the visible region of the spectrum. The fluorescence which arises from f→f transitions within the Ln3+ ion is employed in color television sets, the screens of which contain three phosphor emitters. The red emitter is Eu3+ in Y2 O2 S or Eu3+ :Y2 O3 . The main emissions for Eu3+ are between the 5 Do → 7Fn (n = 4 to 0) levels. The green emitter is Tb3+ in Tb3+ :La2 O2 S. The main emissions for Tb3+ are between the 5 D4 and 7 F (n = 6 to 0) levels. The best blue emitter is Ag, Al:ZnS, which has no Ln3+ n component. 18.1.5

Magnetic properties

The paramagnetism of Ln3+ ions arises from their unpaired 4f electrons which interact little with the surrounding ligands in Ln3+ compounds. The magnetic properties of these compounds are similar to those of the free Ln3+ ions. For most Ln3+ the magnitude of the spin–orbital interaction in f orbital is sufficiently large, so that the excited levels are thermally inaccessible, and hence the magnetic behavior is determined entirely by the ground level. The effective magnetic moment µeff of this level is given by the equation µeff = gJ where gJ =

H

J (J + 1),

3 S(S + 1) − L(L + 1) + . 2 2J (J + 1)

The calculated µeff and observed values from experiments are listed in Table 18.1.4 and shown in Fig. 18.1.2. There is good agreement in all cases except for Sm3+ and Eu3+ , both of which have low-lying excited states (6 H31/2 for Sm3+ , and 7 F1 and 7 F2 for Eu3+ ) which are appreciably populated at room temperature.

687

Structural Chemistry of Selected Elements Magnetic moments / meff

688

Fig. 18.1.2.

Measured and calculated effective magnetic moments (µeff ) of Ln3+ ions at 300 K (broken lines represents the calculated values).

Dy3+ Ho3+ Tb3+ Er3+ Gd3+ Tm3+

10 8 6 4 2

Yb3+

Pr3+ Nd3+ 3+ Pm

Ce3+

0

La3+

Sm3+

Eu3+

Lu3+

0 1 2 3 4 5 6 76 5 4 3 2 10 number of unpaired electrons

18.2

Structure of oxides and halides of rare-earth elements

The bonding in the oxides and halides of rare-earth elements is essentially ionic. Their structures are determined almost entirely by steric factors and gradual variation across the series, and can be correlated with changes in ionic radii. (a)

(b)

Fig. 18.2.1.

La

(a) Structure of La2 O3 and (b) the two coordination environments of Y3+ in the Y2 O3 structure.

18.2.1

Y

Oxides

The sesquioxides M2 O3 are the stable oxides for all rare-earth elements except Ce, Pr, and Tb, and are the final product of calcination of many salts such as oxalates, carbonates, and nitrates. The sesquioxides M2 O3 adopt three structural types: The type-A (hexagonal) structure consists of MO7 units which approximate to capped octahedral geometry, and is favored by the lightest lanthanides (La, Ce, Pr, and Nd). Figure 18.2.1(a) shows the structure of La2 O3 . The type-B (monoclinic) structure is related to type-A, but is more complex as it contains three kinds of non-equivalent M atoms, some with octahedral and the remainder with monocapped trigonal prismatic coordination. In the latter type of coordination geometry, the capping O atom is appreciably more distant than those at the vertices of the prism. For example, in Sm2 O3 , the seventh atom is at 273 pm (mean) and the others are at 239 pm (mean). This type is favored by the middle lanthanides (Sm, Eu, Gd, Tb, and Dy). The type-C (cubic) structure is related to the fluorite structure (Fig. 10.1.6), but with one-quarter of the anions removed in such a way as to reduce the

Rare-Earth Elements metal coordination number from 8 to 6, resulting in two different coordination geometries, as shown in Fig. 18.2.1(b). This type is favored by Sc, Y, and heavy lanthanides from Nd to Lu. The dioxides CeO2 and PrO2 adopt the fluorite structure with cubic unit-cell parameters a = 541.1 and 539.2 pm, respectively, and Tb4 O7 is closely related to fluorite. 18.2.2

Halides

(1) Fluorides Trifluorides are known for all the rare-earth elements. The structure of ScF3 is close to the cubic ReO3 structure [Fig. 10.4.4(a)], in which Sc3+ has octahedral coordination. The YF3 structure has a nine-coordinate Y3+ in a distorted tricapped trigonal prism, eight F− at approximately 230 pm, and the ninth at 260 pm. The YF3 structure type is adopted by the 4f trifluorides from SmF3 to LuF3 . The early light trifluorides from LaF3 to HoF3 adopt the LaF3 structure, in which the La3+ is 11-coordinate with a fully capped, distorted trigonal prismatic coordination geometry. The neighbors of La3+ are seven F− at 242-8 pm, two F− at 264 pm, and a further two F− at 300 pm. Tetrafluorides LnF4 are known for Ce, Pr, and Tb. In the structure for LnF4 , the Ln4+ ion is surrounded by eight F− forming a slightly distorted square antiprism, which shares its vertices with eight others. (2) Chlorides Chlorides ScCl3 , YCl3 , and later LnCl3 (from DyCl3 to LuCl3 ) adopt the YCl3 layer structure, in which the small M3+ ion is surrounded by an octahedron of Cl− neighbors. The early trichlorides (from LaCl3 to GdCl3 ) adopt the LaCl3 structure, in which the large La3+ ion is surrounded by nine approximately equidistant Cl− neighbors in a tricapped trigonal prismatic arrangement. Figure 18.2.2 shows the structure of LaCl3 . Chlorides are also known in oxidation state +2 for Nd, Sm, Eu, Dy, and Tm. The structure of the sesquichloride Gd2 Cl3 is best formulated as (a)

(b)

La Cl

Fig. 18.2.2.

Crystal structures of LaCl3 : (a) viewed along the c axis, and (b) coordination geometry of La3+ .

689

690

Structural Chemistry of Selected Elements (a)

(b)

Gd

Gd Cl Cl

Fig. 18.2.3.

Structure of Gd2 Cl3 : (a) perspective view of a chain aligned along the b axis, and (b) view perpendicular to the b axis.

[Gd4 ]6+ [Cl− ]6 and is made up of infinitive chains of Gd6 octahedra sharing opposite edges, with chlorine atoms capping the triangular faces, as shown in Fig. 18.2.3. (3) Bromides and iodides The trihalides MBr3 and MI3 are known for all the lanthanide elements. The early lanthanide tribromide (La to Pr) adopt the LaCl3 structure, while the later tribromides (from Nd to Lu) and the early triiodides (from La to Nd) form a layer structure with eight-coordinate lanthanide ions. Ionic dibromides and diiodides are known for Nd, Sm, Eu, Dy, Tm, and Yb. SmI2 , EuI2 , and YbI2 are useful starting materials for organometallic compounds of these elements in their +2 oxidation states. Iodide SmI2 is a popular one-electron reducing agent for organic synthesis. The diiodides of La, Ce, Pr, and Gd exhibit metallic properties and are best formulated as Ln3+ (I− )2 e− with delocalized electrons. The reduction chemistry of lanthanide(II) compounds will be discussed in Section 18.5. (4) Oxohalides Many oxohalides of rare-earth elements have been characterized. The crystal of γ -LaOF has a tetragonal unit cell with a = 409.1 pm and c = 583.6 pm, space group P4/nmm. In this structure, each La3+ is coordinated by four O2− and four F− anions, forming a distorted cube, as shown in Fig. 18.2.4. The distance of La–O is 261.3 pm and La–F 242.3 pm.

18.3

Coordination geometry of rare-earth cations

In lanthanide complexes, the Ln ions are hard Lewis acids, which prefer to coordinate hard bases, such as F, O, N ligands. The f-orbitals are not involved to a significant extent in M–L bonds, so their interaction with ligands is almost electrostatic in nature. Table 18.3.1 lists some examples of the various coordination

Rare-Earth Elements

691

O La

F

Fig. 18.2.4.

Structure of γ -LaOF. Table 18.3.1. Coordination number and geometry of rare-earth cations

Oxidation CN Coordination geometry∗ state

Example (structure)

+2

Yb(PPh2 )2 (THF)4 , SmO, EuTe SmI2 (THF)5 SmF2 La[N(SiMe3 )2 ]3 [Fig. 18.3.1(a)] [Lut Bu4 ]− Nd[N(SiHMe2 )2 ]3 (THF)2 GdCl4 (THF)− 2 , ScCl3 , YCl3 , LnCl3 (Dy–Lu) Pr[S2 P(C6 H11 )2 ]3 Gd2 S3 , Y(acac)3 ·H2 O La2 O3 [Fig. 18.2.1(a)] Nd(CH3 CN)(CF3 SO3 )3 L† [Fig. 18.3.1(b)] Lu(S2 CNEt2 )− 4 [La(bipyO2 )4 ]3+ Gd2 S3 Nd(H2 O)3+ 9 , LaCl3 [Fig. 18.2.2] LaCl3 (18C6) [Fig. 18.3.1(c)] Lu(NO3 )2− 5 [Fig. 18.3.1(d)] Eu(NO3 )3 (12C4) LaF3 La(NO3 )3 (15C5) [Fig. 18.3.1(e)] La(NO3 )3− 6 [Fig. 18.3.1(f)] Cs2 CeCl6 Ce(acac)4 CeO2 Ce(NO3 )4 (OPPh3 )2 [Ce(NO3 )6 ]2−

+3

+4

∗ †

6 7 8 3 4 5 6 6 7 7 8 8 8 8 9 9 10 10 11 11 12 6 8 8 10 12

Octahedral Pentagonal bipyramidal Cubic Pyramidal Tetrahedral Trigonal bipyramidal Octahedral Trigonal prismatic Monocapped trigonal prismatic Monocapped octahedral Square antiprismatic Dodecahedral Cubic Bicapped trigonal prismatic Tricapped trigonal prismatic Capped square antiprismatic Bicapped dodecahedral Irregular Fully capped trigonal prismatic Irregular Icosahedral Octahedral Square antiprismatic Cubic Irregular Icosahedral

The polyhedron may exhibit regular or distorted geometry. L = 1-methyl-1,4,7,10-tetraazacyclododecane

numbers and geometries of rare-earth cations, which are determined by three factors: (1) Steric bulk. The ligands are packed around the metal ion in such a way as to minimize interligand repulsion, and the coordination number is determined

692

Structural Chemistry of Selected Elements (a)

(b) CF3 S La

Si

N

Nd N

(c)

(d)

La

O

Cl Lu

N O

(e)

(f)

La La

N

N O O

Fig. 18.3.1.

--

--

Structures of some lanthanide complexes: (a) La[N(SiMe3 )2 ]3 , CN = 3;

−N− −(CH2 − −CH2 − −NH)3 − −CH2 − −CH2 ], CN = 8; (b) Nd(CH3 CN)(CF3 SO3 ·)3 [CH3 − (c) LaCl3 (18C6), CN = 9; (d) [Lu(NO3 )5 ]2− , CN = 10; (e) La(15C5)(NO3 )3 , CN = 11; (f) [La(NO3 )6 ]3− , CN = 12.

by the steric bulk of the ligands. The coordination number varies over a wide range from 3 to 12, and lower coordination numbers can be achieved with very bulky ligand such as hexamethyldisilylamide. In La[N(SiMe3 )2 ]3 , the coordination number is only three, as shown in Fig. 18.3.1(a). (2) Ionic size. The large sizes of lanthanide ions lead to high coordination numbers; eight or nine is very common, and several complexes are known with coordination number 12. For example the NO− 3 ligand, which has a small bite 3+ angle, forms a 12-coordinate La complex. Figures 18.3.1(b) to 18.3.1(f) show

Rare-Earth Elements

693

the structures of Ln3+ complexes with coordination numbers ranging from 8 to 12, respectively. The coordination geometries of high coordination complexes are often irregular. (3) Chelate effect. Higher coordination numbers are usually achieved with 2− chelating ligands, such as crown ethers, EDTA and NO− 3 or CO3 . Cations Ln3+ form a range of complexes with crown ethers. In the crystal structure of La(18C6)(NO3 )3 , the La3+ ion is coplanar with the six O-donors of the crown ether. The flexibility of 18C6 allows it to pucker and bind effectively to the smaller later lanthanides. Dibenzo-18C6 is much less flexible than 18C6, and can only form complexes with large early Ln3+ ions (La to Nd) in the presence 3+ of the strongly coordinating bidentate NO− 3 counterion. Complexes of Ln with 15C5 or 12C4 are known for La–Lu with NO− 3 counterions. The larger Ln3+ ion cannot fit within the cavity of these ligands, so that it sits above the plane of the macrocycle. In the coordination chemistry of rare-earth metals, compounds containing M–M bonds are very rare, but the complexes often exist as dimers or oligomers linked by bridging ligands. Figure 18.3.2 shows the structures of some dimeric and oligomeric coordination compounds: (a) in Rb5 Nd2 (NO3 )11 ·H2 O, one NO− 3 ligand bridges two Nd atoms to form the dimeric anion 5 1 t Nd2 (NO3 )5− 11 ; (b) in the complex [Y(η : η -C5 Me4 SiMe2 N Bu)(µ-C4 H3 S)]2 , a pair of µ-C4 H3 S ligands bridge two Y atoms; (c) in Yb2 (OC6 H3 Ph2 2,6)4 (PhMe)1.5 , two OC6 H3 Ph2 -2,6 ligands bridge two Yb atoms; and (d) in K+ (THF)6 {[MePhC(C4 H3 N)2 ]Sm}5 (µ5 -I− ), the pentameric anion is formed

(a)

(b)

N

Nd

Y

S

Si

N O

(c)

Ph Me

(d) Me Ph O O

O Ar

O

N

N N

N N Sm

Yb Me Ph

N N

N

Ph Me

I N N Me Ph

Fig. 18.3.2.

Structures of some dimeric and oligomeric coordination compound of rare-earth metals: (a) [Nd2 (NO3 )11 ]5− , (b) [Y( η5 : η1 -C5 Me4 SiMe2 Nt Bu)(µ-C4 H3 S)]2 , (c) Yb2 (2,6-Ph2 C6 H3 O)4 , OAr = (2,6-Ph2 C6 H3 O); (d) {[MePhC(C4 H3 N)2 ]Sm}5 (µ5 -I− ).

694

Structural Chemistry of Selected Elements by five bridging [MePhC(C4 H3 N)2 ] ligands and consolidated by a central µ5 -I− anion. The lanthanide complexes exhibit a number of characteristic features in their structures and properties: (a) There is a wide range of coordination numbers, generally 6 to 12, but 3 to 5 are known, as listed in Table 18.3.1. (b) Coordination geometries are determined by ligand steric factors rather than crystal field effects. For example, the donor oxygen atoms in different ligands coordinate to the La3+ ions in different geometries: monocapped octahedral (CN = 7), irregular (CN = 11), and icosahedral (CN = 12). (c) The lanthanides prefer anionic ligands with hard donor atoms of rather high electronegativity (e.g., oxygen and fluorine) and generally form labile “ionic” complexes that undergo facile ligand exchange. (d) The lanthanides do not form Ln=O or Ln≡N multiple bonds of the type known for many transition metals and certain actinides. (e) The 4f orbitals in the Ln3+ ions do not participate directly in bonding. Their spectroscopic and magnetic properties are thus largely unaffected by the ligands.

18.4

Organometallic compounds of rare-earth elements

In contrast to the extensive carbonyl chemistry of the d-transition metals, lanthanide metals do not form complexes with CO under normal conditions. All organolanthanide compounds are highly sensitive to oxygen and moisture, and in some cases they are also thermally unstable. Organolanthanide chemistry has mainly been developed using the cyclopentadienyl C5 H5 (Cp) group and its substituted derivatives, such as C5 Me5 (Cp*), largely because their size allows some steric protection of the large metal center. 18.4.1

Cyclopentadienyl rare-earth complexes

The properties of cyclopentadienyl lanthanide compounds are influenced markedly by the relationship between the size of the lanthanide atoms and the steric demand of the Cp group. The former varies from La to Lu according to lanthanide contraction, while the latter varies from the least bulky Cp to highly substituted Cp*, which is appreciably larger. The Sc and Y complexes are very similar to those of lanthanides with proper allowance for the relative atomic sizes. (1) Triscyclopentadienyl complexes In LaCp3 , the coordination requirements of the large La3+ ion are satisfied by formation of a polymer, where each La atom is coordinated to three η5 -C5 H5 ligands with an additional η2 -C5 H5 interaction, as shown in Fig. 18.4.1(a). The intermediate-size Sm atom forms a simple Sm(η5 -C5 H5 )3 monomeric species, as shown in Fig. 18.4.1(b). The smallest lanthanide, Lu, is unable to accommodate three η5 -C5 H5 ligands, so that LuCp3 adopts a polymeric structure with

Rare-Earth Elements (a)

La

La

La

(b)

Sm

(c)

Lu

Lu

Fig. 18.4.1.

Structural formulas and geometries of LnCp3 complexes: (a) LaCp3 , (b) SmCp3 , and (c) LuCp3 .

each Lu coordinated to two η5 -C5 H5 ligands and two µ2 -Cp ligands, as shown in Fig. 18.4.1(c). (a)

(b)

Pr

Sm C

N Cl

Fig. 18.4.2.

Structure of (a) Cp3 Pr(CNC6 H11 ) and (b) [Cp3 SmClSmCp3 ]− .

Many adducts of LnCp3 with neutral Lewis bases (such as THF, esters, phosphines, pyridines, and isocyanides) have been prepared and characterized. These complexes usually exhibit pseudo-tetrahedral geometry. Figure 18.4.2(a) shows the structure of Cp3 Pr(CNC6 H11 ) and Fig. 18.4.2(b) shows the structure of the anion of [Li(DME)3 ]+ [Cp3 SmClSmCp3 ]− , in which two Cp3 Ln fragments are bridged by one anionic ligand.

695

696

Structural Chemistry of Selected Elements

Yb C

Sc

H

Cl

(a)

Be

(b)

Cl Lu

O Yb Te

Fig. 18.4.3.

Structures of some biscyclopentadienyl rare-earth complexes: (a) (Cp2 ScCl)2 , (b) Cp∗2 Yb(MeBeCp∗ ), (c) Cp2 LuCl(THF), and (d) (Cp∗2 Yb)2 Te2 .

(c)

18.4.2

(d)

Biscyclopentadienyl complexes

Many crystal structures of the biscyclopentadienyl rare-earth compounds have been determined; four examples are shown in Fig. 18.4.3. (a) (Cp2 LnCl)2 The configuration of dimers of this type is dependent on the relative importance of the steric interaction of the Cp rings with the halide bridge versus the interaction between the Cp rings on both metal centers. In (Cp2 ScCl)2 , the Cp ring is relatively small in comparison with the halide ligand; accordingly all Cp centroids lie in one plane, and the Sc2 Cl2 plane is perpendicular to it, as shown in Fig. 18.4.3(a). (b) Cp∗2Yb(MeBeCp∗ ) The Cp∗2Yb unit can be coordinated by saturated hydrocarbons, as in MeBeCp∗ . The positions of the hydrogens on the bridging methyl group show that this is not a methyl bridge having a 3c-2e bond between Yb–C–Be, as shown in Fig. 18.4.3(b). (c) Cp2 LuCl(THF) This adduct is monomeric with one coordinated THF, forming a pseudotetrahedral arrangement (each Cp− ligand is considered to be tridentate), as shown in Fig. 18.4.3(c). (d) (Cp∗2Yb)2 Te2 In the chalcogenide complex Cp∗2Yb(Te2 )YbCp∗2 , the Te2 unit serves as a bridging ligand, as shown in Fig. 18.4.3(d).

Rare-Earth Elements

697

Cl Er O

Fig. 18.4.4.

Structure of CpErCl2 (THF)3 .

(3) Monocyclopentadienyl complexes Since monocyclopentadienyl rare-earth complexes require four to six σ -donor ligands to reach the stable coordination numbers 7 to 9, monomeric complexes must bind several neutral donor molecules. Generally, some of these donor molecules are easily lost, and dinuclear and polynuclear complexes are formed. This accounts for the fact that monocyclopentadienyl rare-earth complexes exhibit rich structural complexity. Figure 18.4.4 shows the structure of CpErCl2 (THF)3 . 18.4.3

Benzene and cyclooctatetraenyl rare-earth complexes

All the lanthanides and Y are able to bind two substituted benzene rings, such as Gd(η6 -C6 H3 t Bu3 )2 and Y(η6 -C6 H6 )2 . Figure 18.4.5(a) shows the sandwich structure of Gd(η6 -C6 H3 t Bu3 )2 . In this complex, the Gd center is zero-valent. The large lanthanide ions are able to bind a planar cyclooctatetraene dianion ligand, as shown in Fig. 18.4.5(b) to Fig. 18.4.5(d). In [(C8 H8 )2 Ce]K[CH3 O(CH2 CH2 O)2 CH3 ], Ce(III) is sandwiched by two (η8 -C8 H8 ) dianions, as shown in Fig. 18.4.5(b). The structure of (C8 H8 )3 Nd2 (THF)2 shows a [(C8 H8 )2 Nd]− anion coordinating to the [(C8 H8 )Nd(THF)2 ]+ cation via two carbon atoms of the C8 H2− 8 ligand, as shown in Fig. 18.4.5(c). In the sandwich complex (C8 H8 )Lu(Cp∗ ), as shown in Fig. 18.4.5(d), the molecular structure is slightly bent with a ring centroid–Lu–ring centroid angle of 173◦ . The methyl groups of Cp∗ are bent away from the Lu center by 0.7◦ -2.3◦ from the idealized planar configuration. The averaged Lu–C bond distances for ∗− ligands are 243.3 and 253.6 pm, respectively. the C8 H2− 8 and Cp 18.4.4

Rare-earth complexes with other organic ligands

A variety of “open” π complexes, such as allyl complexes, are known. Generally, the allyl group is η3 -bound to the rare-earth center. Figure 18.4.6(a) shows the structure of the anion in [Li2 (µ-C3 H5 )(THF)3 ]+ [Ce(η3 -C3 H5 )4 ]− . Using bulky ligands or chelating ligands to saturate the complexes coordinatively or sterically, the rare-earth complexes without π ligands have been obtained and characterized. The La and Sm complexes with bulky alkyl ligands

698

Structural Chemistry of Selected Elements (a)

(b)

O

K Gd

Ce

(c)

(d)

Nd

Lu O

Fig. 18.4.5.

Structures of (a) Gd(η6 -C6 H3 t Bu3 )2 , (b) [(C8 H8 )2 Ce]K[CH3 O(CH2 CH2 O)2 CH3 ], (c) (C8 H8 )3 Nd2 (THF)2 , and (d) (C8 H8 )Lu(Cp∗ ).

(a)

(b)

(c)

Sm

Si

Ce

Fig. 18.4.6.

Structures of some rare-earth complexes: (a) [Ce(η3 -C3 H5 )4 ]− , (b) Sm[CH(SiMe3 )2 ]3 , and (c) [Lu(t Bu)4 ]− .

Lu

Rare-Earth Elements [CH(SiMe3 )2 ] are pyramidal, being stabilized by agostic interactions of methyl groups with the highly Lewis acidic metal center, as shown in Fig. 18.4.6(b). The second half of the lanthanide series react with the more bulky t BuLi reagent to form tetrahedrally coordinated complexes, such as [Li(TMEDA)2 ]+ [Lu(t Bu)4 ]− . Figure 18.4.6(c) shows the structure of the anion [Lu(t Bu)4 ]− .

18.5

Reduction chemistry in oxidation state +2

Only the elements samarium, europium, and ytterbium have significant “normal” chemistry based on true Ln2+ ions, although SmCl2 and EuCl2 are well-characterized and have been known for over a century. The compounds of Pr, Nd, Dy, Ho, and Tm in oxidation state +2 are unstable in aqueous solution. Lanthanide(II) compounds are of current interest as reductants and coupling agents in organic and main-group chemistry.

18.5.1

Samarium(II) iodide

SmI2 , which can be prepared conveniently from samarium powder and 1,2diiodoethane in THF, finds application as a versatile one-electron reducing agent in organic synthesis. Two typical synthetic procedures mediated by SmI2 are the pinacol coupling of aldehydes and the Barbier reaction, as shown in the following schemes:

2 R

SmI2

O

2 SmI2 H

O R

+ H

R

SmI2

SmI2

SmI2

O

O

O

H

R

HO

OH

R

R

R

pinacol coupling

O R1

R2

+ RX

R

2 SmI2 R1

OH R2

SmI2 SmI2X + [R ]

SmI2

O R1

R2

R-SmI2

Barbier reaction

SmI2 reacts with a variety of donor solvents to form crystalline solvates. SmI2 (Me3 CCN)2 is an iodo-bridged polymeric solid containing six-coordinate Sm2+ centers. In contrast, SmI2 (HMPA)4 , where HMPA is (Me3 N)3 P=O, is a discrete six-coordinate molecule with a linear I–Sm–I unit. The diglyme solvate SmI2 [O(CH2 CH2 OMe)2 ]2 exhibits eight-coordination.

699

700

Structural Chemistry of Selected Elements 18.5.2

Decamethylsamarocene

The organosamarium(II) complex Sm(η5 -C5 Me5 )2 has the bent-metallocene structure, which can be attributed to polarization effects; its THF solvate Sm(η5 -C5 Me5 )2 (THF)2 exhibits the expected pseudo-tetrahedral coordination geometry. [Sm(η5 -C5 Me5 )2 ] is a very powerful reductant, and its notable reactions include the reduction of aromatic hydrocarbons such as anthracene and of dinitrogen, as illustrated in the following scheme: Cp*

Cp*

Sm

Cp* Sm Cp*

Cp*2Sm

Cp*

N2

Sm

(Cp* = C5Me5)

Cp*

Cp*

N Sm N

Cp*

The N–N distance in the dinuclear N2 complex is 129.9 pm, as compared with the bond length of 109.7 pm in dinitrogen, and is indicative of a considerable decrease in bond order. An analogous planar system comprising a side-on bonded µ-(bis-η2 )-N2 ligand between two metal centers, with a much longer N–N bond length of 147 pm, occurs in [Cp,,2 Zr]2 (N2 ), as described in Section 15.1.3. (1) Diiodides of thulium, dysprosium, and neodymium The molecular structures of LnI2 (DME)3 (Ln = Tm, Dy; DME = dimethoxyethane) are shown in Fig. 18.5.1(a) and (b). The larger ionic size of Dy2+ compared with Tm2+ accounts for the fact that the thulium(II) complex is seven-coordinate, whereas the dysprosium(II) complex is eight-coordinate. The complex NdI2 (THF)5 has pentagonal bipyramidal geometry with the iodo ligands occupying the axial positions. Thulium(II) complexes are stabilized by phospholyl or arsolyl ligands that can be regarded as derived from the cyclopentadienyl group by replacing one CH group by a P or As atom. Their decreased π-donor capacity relative to the parent cyclopentadienyl system enhances the stability of the Tm(II) center, and stable complexes of the bent-sandwiched type have been isolated. C

(a)

(b) O

I

C I

Tm

Fig. 18.5.1.

Comparison of the molecular structures of (a) hepta-coordinate TmI2 (DME)3 and (b) octa-coordinate DyI2 (DME)3 .

O Dy

Rare-Earth Elements Me TmI2(THF)n

+

Z

Me Et2O

2 K+

Me3Si

Z

Tm THF

SiMe3

Z

Z = P, As

The LnI2 (Ln = Tm, Dy, Nd) species have been used in a wide range of reactions in organic and organometallic syntheses, including the reduction of aromatic hydrocarbons and the remarkable reductive coupling of MeCN to form a tripodal N3 -ligand, as shown in the following schemes:

THF

I

I

Tm

Tm

THF

TmI2 THF

3+

Me Me

Me LnI2 (Ln = Tm, Dy)

MeCN HN

NH2

NH

I–

3

Ln(NCMe)6

References 1. H. C. Aspinall, Chemistry of the f-Block Elements, Gordon and Breach, Amsterdam, 2001. 2. S. Cotton, Lanthanide and Actinide Chemistry, Wiley, Chichester, 2006. 3. N. Kaltsoyannis and P. Scott, The f Elements, Oxford University Press, Oxford, 1999. 4. S. D. Barrett and S. S. Dhesi, The Structure of the Rare-Earth Metal Surfaces, Imperial College Press, London, 2001. 5. A. F. Wells, Structural Inorganic Chemistry, 5th edn., Oxford University Press, Oxford, 1984. 6. C. E. Housecroft and A. G. Sharpe, Inorganic Chemistry, 2nd edn., Prentice-Hall, Harlow, 2004. 7. D. F. Shriver, P. W. Atkins, T. L. Overton, J. P. Rourke, M. T. Weller and F. A. Armstrong, Inorganic Chemistry, 4th edn., University Press, Oxford, 2006. 8. C. H. Huang, Coordination Chemistry of Rare-Earth Elements (in Chinese), Science Press, Beijing, 1997. 9. R. B. King (editor-in-chief), Encyclopedia of Inorganic Chemistry, Wiley, Chichester, 1994. 10. K. A. Gschneidner, Jr., L. Eyring, G. R. Choppin and G. H. Lander (eds.), Handbook on the Physics and Chemistry of Rare Earths, Vol. 18: Lanthanides/Actinides: Chemistry, North-Holland, Amsterdam, 1994.

701

702

Structural Chemistry of Selected Elements 11. J. A. McCleverty and T. J. Meyer (editors-in-chief), Comprehensive Coordination Chemistry II, vol. 3 (G. F. R. Parkin, volume editor), Elsevier-Pergamon, Amsterdam, 2004. 12. E. W. Abel, F. G. A. Stone and G. Wilkinson (editors-in-chief), Comprehensive Organometallic Chemistry II, vol. 4 (M. F. Lappert, volume editor), Pergamon, Oxford, 1995. 13. Thematic issue on “Frontiers in Lathanide Chemistry,” Chem. Rev. 102, no. 6, 2002.

Metal–Metal Bonds and Transition-Metal Clusters

19.1

Bond valence and bond number of transition-metal clusters

A dinuclear transition-metal complex contains two transition-metal atoms each surrounded by a number of ligands. A transition-metal cluster has a core of three or more metal atoms directly bonded with each other to form a discrete molecule containing metal–metal (M–M) bonds. The first organometallic complex reported to possess a M–M bond was Fe2 (CO)9 . Since this Fe–Fe bond is supported by three bridging CO ligands, as shown in Fig. 19.1.1(a), it cannot be taken as definitive proof of direct metal–metal interaction. In contrast, the complexes Re2 (CO)10 , Mn2 (CO)10 , and [MoCp(CO)3 ]2 , with no bridging ligands, provide unequivocal examples of unsupported M–M bonding. In these species the metal atoms are considered to be bonded through a single bond of the 2c-2e type. Figure 19.1.1(b) shows the molecular structure of Mn2 (CO)10 . Since polynuclear complexes and cluster compounds are in general rather complicated species, the application of quantitative methods for describing bonding is not only difficult but also impractical. Qualitative approaches and empirical rules often play an important role in treating such cases. We have used the octet rule and bond valence to describe the structure and bonding of boranes and their derivatives (Sections 13.3 and 13.4). Now we use the 18-electron rule and bond valence to discuss the bonding and structure of polynuclear transition-metal complexes and clusters. The metal atoms in most transition-metal complexes and clusters obey the 18-electron rule. The bond valence, b, of the skeleton of complex [Mn Lp ]q− can be calculated from the formula b = 1/2(18n − g), where g is the total number of valence electrons in the skeleton of the complex, which is the sum of the following three parts: (a) n times the number of valence electrons of metal atom M; (b) p times the number of valence electrons donated to the metal atoms by ligand L; and (c) q electrons from the net charge of the complex.

19

704

Structural Chemistry of Selected Elements (a)

(b)

Fe

Mn

C

O

Fig. 19.1.1.

Structure of dinuclear transition metal complexes: (a) Fe2 (CO)9 and (b) Mn2 (CO)10 .

The bond valence b of the skeleton of a complex or cluster corresponds to the sum of the bond numbers of the metal–metal bonds. For a M–M single bond, the bond number is equal to 1; similarly, the bond number is 2 for a M=M double bond, 3 for a M≡M triple bond, 4 for a M= =M quadruple bond, and 2 for a 3c-2e MMM bond. The majority of cluster compounds have carbonyl ligands coordinated to the metal atoms. Some clusters bear NO, CNR, PR3 , and H ligands, while others contain interstitial C, N, and H atoms. The compounds can be either neutral or anionic, and the common structural metal building blocks are triangles, tetrahedra, octahedra, and condensed clusters derived from them. The carbonyl ligand has two special features. First, the carbonyl ligand functions as a two-electron donor in the terminal-, edge-, or face-bridging mode, and neither changes the valence of the metal skeleton nor requires the involvement of additional ligand electrons. In contrast, the Cl ligand may change from a one- (terminal) to a three- (edge-bridging) or five- (face-bridging) electron donor. Second, the synergic bonding effects which operate in the alternative bridging modes of the carbonyl ligand lead to comparable stabilization energies and therefore readily favor the formation of transition-metal cluster compounds. As mentioned in Sections 13.3 and 13.4, the structures of most known boranes and carboranes are based on the regular deltahedron and divided into three types: closo, nido, and arachno. In a closo-structure the skeletal B and C atoms occupy all the vertices of the polyhedron. In the cases of nido- and arachno-structures, one and two of the vertices of the appropriate polyhedron remain unoccupied, respectively. On each skeletal B and C atom, there is always a H atom (or some other simple terminal ligand such as halide) that points away from the center of the polyhedron and is also linked to the skeleton by a radial 2c-2e single bond. In a polyhedron of n vertices, there are 4n atomic orbitals. Among them, n orbitals are used up for n terminal B–H bonds, the remaining 3n atomic orbitals being available for skeletal bonding. In the skeleton of closo-borane Bn H2− n , there are 4n + 2 valence electrons (n B atoms contribute 3n electrons, n H atoms donate n electrons, and the charge accounts for 2 electrons), and hence 2n + 2 electrons or n + 1 electron pairs are available for skeletal bonding. These numbers are definite. For the transition-metal cluster compounds, however, the

Metal–Metal Bonds electron counts vary with different bonding types. For example, octahedral M6 clusters of different compounds form various structures and bond types. Some examples are discussed below and shown in Fig 19.1.2. Figure 19.1.2(a) shows the structure of [Mo6 (µ3 -Cl)8 Cl6 ]2− . In this structure, eight µ3 -Cl and six terminal Cl atoms are coordinated to the Mo6 cluster. Each µ3 -Cl donates five electrons and each terminal Cl donates one electron. Thus the g value is g = 6 × 6 + (8 × 5 + 6 × 1) + 2 = 84. The bond valence of the Mo6 cluster is b = 1/2(6 × 18 − 84) = 12. The bond valence b precisely matches 12 2c-2e Mo–Mo bonds, as shown in the front and back views of the Mo6 cluster on the right side of Fig. 19.1.2(a). Figure 19.1.2(b) shows the structure of [Nb6 (µ2 -Cl)12 Cl6 ]4− . In this structure, there are 12 µ2 -Cl atoms each donating 3 electrons, plus six terminal µ1 -Cl atoms, each donating one electron, to the Nb cluster. The g value is g = 6 × 5 + (12 × 3 + 6 × 1) + 4 = 76. The bond valence of the Nb6 cluster is b = 1/2(6 × 18 − 76) = 16. In this Nb6 cluster, each edge is involved in bonding with a µ2 -Cl ligand, so the edges do not correspond to 2c-2e Nb–Nb bonds. Each face of the Nb6 cluster forms a 3c-2e NbNbNb bond, and has bond number 2. The sum of bond number, 16, is just equal to the bond valence of 16, as shown in the front and back views of the Nb cluster in Fig. 19.1.2(b). Figure 19.1.2(c) shows the structure of Rh6 (µ3 -CO)4 (CO)12 . The CO group as a ligand always donates two electrons to the Mn cluster. The g value and bond valence of the Rh6 cluster are b = 1/2(6 × 18 − 86) = 11 The b value of Rh6 is 11, which just matches the b value of B6 H2− 6 . The Rh6 cluster is stabilized by four 3c-2e RhRhRh bonds and three 2c-2e Rh-Rh bonds. Various bond formulas can be written for the Rh6 cluster, one of which is shown on the right side of Fig. 19.1.2(c). These formulas are equivalent by resonance and the octahedron has overall Oh symmetry. 19.2

Dinuclear complexes containing metal–metal bonds

Studies on dinuclear transition-metal compounds containing metal–metal bonds have deeply enriched our understanding of chemical bonding. The nature and

705

706

Structural Chemistry of Selected Elements (a) 1

1

6 4

1 2

2

5

4

4

2 6

5

3

3

3

(b) 1

1 6

4

2

4 2

5 3

1 4

2

5

6

3

3

(c)

1 5 6

4

1

1

2 4

2

2

4

6

5 3

3

3

Fig. 19.1.2.

Structure and bonding of three octahedral clusters: (a) [Mo6 (µ3 -Cl)8 Cl6 ]2− ; (b) [Nb6 (µ2 -Cl)12 Cl6 ]4− ; and (c) Rh6 (µ3 -CO)4 (CO)12 .

implication of M–M bonds are richer and more varied than the covalent bonds of the second-period representative elements. The following points may be noted. (a) The d atomic orbitals of transition metals are available for bonding, in addition to the s and p atomic orbitals. (b) The number of valence orbitals increases from 4 for the second-period elements to 9 for the transition-metal atoms. Thus the octet rule suits the former and eighteen-electron rule applies to the latter. (c) The use of d-orbitals for bonding leads to the possible formation of a quadruple bond (and even a quintuple bond) between two metal atoms, in addition to the familiar single, double, and triple bonds.

Metal–Metal Bonds (d) The transition-metal atoms interact with a large number of ligands in coordination compounds. The various geometries and electronic factors have significant effects on the properties of metal–metal bonds. The 18-electron rule is not strictly valid, thus leading to varied M–M bond types.

19.2.1

Dinuclear transition-metal complexes conforming to the 18-electron rule

When the structure of a dinuclear complex has been determined, the structural data may be used to enumerate the number of valence electrons available in the complex, to determine its bond valence, and to understand the properties of the metal–metal bond. For a dinuclear complex, the bond valence b = 1/2(18 × 2 − g). Table 19.2.1 lists the data for some dinuclear complexes. In the complex Ni2 (Cp)2 (µ2 -PPh2 )2 , with two bridging ligands (µ2 -PPh2 ) linking the Ni atoms, the bond valence equals zero, indicating that there is no bonding interaction between them. Mn2 (CO)10 is one of the simplest dimeric compounds containing a metal– metal single bond unsupported by bridging ligands, and its diamagnetic behavior is accounted for in compliance with the 18-electron rule. The structures of Tc2 (CO)10 , Re2 (CO)10 , and MnRe(CO)10 , which are isomorphous with Mn2 (CO)10 , have also been determined. The measured M–M bond lengths (pm) are Tc–Tc 303.6, Re–Re 304.1, and Mn–Re 290.9. The structure of Fe2 (CO)9 , shown in Fig. 19.1.1(a), has an Fe–Fe single bond of 252.3 pm, which is further stabilized by the bridging carbonyl ligands. Many dinuclear complexes have a M=M double bond. Some examples are Co2 (CO)2 Cp∗2 , Co=Co 233.8pm; Fe2 (NO)2 Cp2 , Fe=Fe 232.6pm; Re2 (µ-Cl)2 Cl4 (dppm)2 , Re=Re 261.6pm; Mo2 (OR)8 (R = i Pr, t Bu), Mo=Mo 252.3pm. Most compounds with triple and quadruple bonds are formed by Re, Cr, Mo, and W. The ligands in such compounds are in general relatively hard Lewis bases such as halides, carboxylic acids, and amines. Nevertheless, in some cases π-acceptor ligands such as carbonyl, phosphines and nitrile are also present. Table 19.2.1. Dinuclear complexes

Complex

g

b

M–M(pm)

Bond properties

Ni2 (Cp)2 (µ2 -PPh2 )2 (CO)5 Mn2 (CO)5 Co2 (µ2 -CH2 ) (µ2 -CO)(Cp∗ )2 Cr2 (CO)4 (Cp)2 [Mo2 (µ2 -O2 CMe)2 (MeCN)6 ]2+

36 34 32 30 28

0 1 2 3 4

336 289.5 232.0 222 213.6

Ni· · · Ni, no bonding Mn–Mn, single bond Co=Co, double bond Cr≡Cr, triple bond Mo= =Mo, quadruple bond

707

708

Structural Chemistry of Selected Elements 19.2.2

Quadruple bonds

The recognition and understanding of the quadruple bond is one of the most important highlights in modern inorganic chemistry. The overlap of d atomic orbitals can generate three types of molecular orbitals: σ, π, and δ. These molecular orbitals can be used to form a quadruple bond between two transition-metal atoms under appropriate conditions. In a given compound, however, not all of these orbitals are always available for multiple metal–metal bonding. Thus the 18-electron rule does not always hold for the dinuclear complexes and needs to be modified according to their structures. The most interesting aspect of the crystal structure of K2 [Re2 Cl8 ]·2H2 O is the presence of the dianion Re2 Cl2− 8 (Fig. 19.2.1), which possesses an extremely short Re–Re bond distance of 224.1 pm, as compared with an average Re–Re distance of 275 pm in rhenium metal. Another unusual feature is the eclipsed configuration of the Cl atoms with a Cl· · · Cl separation of 332 pm.As the sum of van der Waals radii of two Cl atoms is 360 pm, the staggered configuration would normally be expected for Re2 Cl2− 8 . These two features are both attributable to the formation of a Re= =Re quadruple bond. The bonding in the skeleton of the [Re2 Cl8 ]2− ion can be formulated as follows: each Re atom uses its square-planar set of dsp2 (dx2 −y2 , s, px , py ) hybrid orbitals to overlap with ligand Cl p orbitals to form Re–Cl bonds. The pz atomic orbital of Re is not available for bonding. The remaining dz2 , dxz , dyz , and dxy atomic orbitals on each Re atom overlap with the corresponding orbitals on the other Re atom to generate the following MOs: dz2 ± dz2

→

σ and σ∗ MO

dyz ± dyz

→

π and π∗ MO

dxz ± dxz

dxy ± dxy

→

π and π∗ MO

→

δ and δ∗ MO

Figure 19.2.2 shows the pairing up of d AO’s of two Re atoms to form MO’s and the ordering of the energy levels. In the [Re2 Cl8 ]2− ion, the two Re atoms have 16 valence electrons including two from the negative charge. Eight valence electrons are utilized to form eight Re–Cl bonds, and the remaining eight occupy four metal–metal bonding orbitals to form a quadruple bond: one σ bond, two π bonds, and one δ bond, leading to the σ2 π 4 δ2 configuration. 332 pm

Cl

x

224 pm Re 229 pm Fig. 19.2.1.

Structure of [Re2 Cl8 ]2− .

y z

Metal–Metal Bonds dz2 – dz2

dyz – dyz

dxz – dxz

dxy – dxy

!

!

" ! ! " " ! ! "

" !

"

"

! "

"

!

!

"

dyz + dyz

" !

+

"

! "

! " " !

"

"

)*

! "

**

! "

! "

*

)

" !

dxz + dxz

" ! ! "

+

! " " !

dz2 + dz2

!

+

!

!

(*

" !

!

+

!

! "

!

dxy + dxy

!

"

709

!

(

The structures of two transition-metal complexes that contain a Mo= =Mo quadruple bond are shown in Fig. 19.2.3. In the compound [Mo2 (O2 CMe)2 (NCMe)6 ](BF4 )2 , each Mo atom is six-coordinate, and all nine valence AO’s are used for bonding according to the 18-electron rule. In the cation [Mo2 (O2 CMe)2 (NCMe)6 ]2+ , g = 2 × 6 + 2 × 3 + 6 × 2 − 2 = 28,

and

b = 1/2(2 × 18 − 28) = 4. The Mo–Mo bond distance of 213.6 pm is in accord with the quadruple Mo= =Mo bond. In the molecule Mo2 (O2 CMe)4 , each Mo atom is five-coordinate and has one empty AO(pz ) which is not used for bonding. It obeys the 16-electron rule with g = 2 × 6 + 4 × 3 = 24 and b = 1/2(2 × 16 − 24) = 4. The observed Mo–Mo distance of 209.3 pm is consistent with that expected of a quadruple bond. A large number of dinuclear complexes containing a M= =M quadruple bond formed by the Group 16 and 17 metals Cr, Mo, W, Re, and Tc have been reported in the literature. Selected examples are listed in Table 19.2.2.

Fig. 19.2.2.

Overlap of d orbitals leading to the formation of a quadruple bond between two metal atoms. Note that the z axis of each metal atom is taken to point toward the other, such that if a right-handed coordinate system is used for the atom on the left, a left-handed coordinate system must be used for the atom on the right.

710

Structural Chemistry of Selected Elements Table 19.2.2. Compounds containing a M≡M quadruple bond

Compound

M= =M

Distance(pm)

Rule

g

Cr2 (2-MeO-5-Me-C6 H3 )4 Cr2 [MeNC(Ph)NMe]4 Cr2 (O2 CMe)4 Cr2 (O2 CMe)4 (H2 O)2 Mo2 (hpp)4 ∗ K4 [Mo2 (SO4 )4 ]·2H2 O [Mo2 (O2 CCH2 NH3 )4 ]Cl4 · 3H2 O Mo2 [O2 P(OPh)2 ]4 W2 (hpp)4 · 2NaHBEt3 W2 (O2 CPh)4 (THF)2 W2 (O2 CCF3 )4 W2 Cl4 (PBun3 )4 · C7 H8 (Bu4 N)2 Tc2 Cl8 K2 [Tc2 (SO4 )4 ]·2H2 O Tc2 (O2 CCMe3 )4 Cl2 (Bu4 N)2 Re2 F8 · 2Et2 O Na2 [Re2 (SO4 )4 (H2 O)2 ]· 6H2 O [Re2 (O2 CMe)2 Cl4 (µ-pyz)]n

Cr= =Cr Cr= =Cr Cr= =Cr Cr= =Cr Mo= =Mo Mo= =Mo Mo= =Mo Mo= =Mo W= =W W= =W W= =W W= =W Tc= =Tc Tc= =Tc Tc= =Tc Re= =Re Re= =Re Re= =Re

182.8 184.3 228.8 236.2 206.7 211.0 211.2 214.1 216.1 219.6 222.1 226.7 214.7 215.5 219.2 218.8 221.4 223.6

16e 16e 16e 18e 16e 18e 16e 16e 16e 18e 16e 16e 16e 16e 18e 16e 18e 18e

24 24 24 28 24 28 24 24 24 28 24 24 24 24 28 24 28 28

∗ hpp is the anion of 1,3,4,6,7,8-hexahydro-2H -pyrimido-[1,2-a]-pyrimidine (Hhpp); pyz is pyrazine.

The quadruple bond can undergo a variety of interesting reactions, as outlined in Fig. 19.2.4. (1) There is a rich chemistry in which ligands are exchangable, and virtually every type of ligand can be used except the strong π acceptors. (2) Addition of a mononuclear species to an M= =M bond can yield a trinuclear cluster. (3) Two quadruple bonds can combine to form a metallacyclobutadiyne ring. (4) Oxidative addition of acids to generate a M≡M bond (particularly W≡W) is a key part of molybdenum and tungsten chemistry. (5) Phosphines can act as reducing agents as well as ligands to give products with triple bonds of the σ2 π4 δ2 δ∗2 type, as in Re2 Cl4 (PEt3 )4 . (6) Photo excitation by the δ → δ∗ transition can lead to reactive species which are potentially useful in photosensitizing various reactions, including the splitting of water. (a)

(b)

O

O 213.6

209.3

Mo N

Fig. 19.2.3.

Structure of (a) [Mo2 (O2 CMe)2 (NCMe)6 ]2+ and (b) Mo2 (O2 CMe)4 .

Mo

Metal–Metal Bonds Coordination chemistry substitution reactions Mononuclear complexes

CO, NO, RNC

(8)

Lower bond order

±e (7) hv (6)

M M

M

M (1)

M M σ3π4δ2

(2) M

M

(3)

(5) PR3 (4)

Reactive excited state

M

M

M

M

H+ Fig. 19.2.4.

H M2X4(PR3)4 σ2π4δ2δ*2

M

M

(7) Electrochemical oxidation or reduction reduces the bond order and generates reactive intermediates. (8) With π-acceptor ligands, the M= =M bonds are usually cleaved to give mononuclear products, which are sometimes inaccessible by any other synthetic route. 19.2.3

Bond valence of metal–metal bond

In dinuclear complexes, the bond valence of the metal–metal (M–M) bond can be calculated from its number of bonding electrons, gM . A simple procedure for counting the metal–metal bond valence is as follows: (a) Calculate the g value in the usual manner. (b) Calculate the number of valence electron used for M–L bonds, gL. (c) Calculate the number of valence electron used for M–M bonds, gM = g − gL . (d) Assign the gM electrons to the following orbitals according to the energy sequence: σ, (πx , πy ), δ, δ∗ , (π∗x , π∗y ), and σ∗ , as shown in Fig. 19.2.2. Some examples are presented below: (1) Mo2 (O2 CMe)4 g = 2 × 6 + 4 × 3 = 24,

gL = 8 × 2 = 16,

gM = g − gL = 24 − 16 = 8.

The electronic configuration is σ2 π4 δ2 , and the bond order is 4; i.e., the bond valence is 4. For this Mo= =Mo bond, the bond length is 209.3 pm. (2) Mo2 (O2 CMe)2 (MeCN)6 ]2+ g = 2 × 6 + 2 × 3 + 6 × 2 − 2 = 28, gM = 28 − 20 = 8.

711

gL = 2 × 5 × 2 = 20,

The electronic configuration is σ2 π4 δ2 , and the bond valence is 4. So again this is a Mo= =Mo bond, and the bond length is 213.6 pm.

Some reaction types of dimetal compounds containing a M≡M quadruple bond.

712

Structural Chemistry of Selected Elements (a)

(b) C 216.7 pm

223.2 pm Re

Mo

P

Fig. 19.2.5.

Structure of (a) Re2 Cl4 (PEt3 )4 and (b) Mo2 (CH2 SiMe3 )6

Cl

(3) Re2 Cl4 (PEt 3 )4 g = 2 × 7 + 4 × 1 + 4 × 2 = 26,

gL = 8 × 2 = 16,

gM = 26 − 16 = 10.

The structure of the molecule is shown in Fig. 19.2.5(a). The electronic configuration is σ2 π4 δ2 δ*2 . The bond valence is 3, indicating a Re≡Re triple bond, and the bond length is 223.2 pm. (4) Mo2 (CH2 SiMe3 )6 The molecule has D3d symmetry, as shown in Fig. 19.2.5(b). g = 2 × 6 + 6 × 1 = 18,

gL = 6 × 2 = 12,

gM = 18 − 12 = 6.

The electronic configuration is σ2 π4 . The length of the Mo≡Mo triple bond is 216.7 pm. (5) Mo2 (OR)8 , (R = i Pr, t Bu) g = 2 × 6 + 8 × 1 = 20,

gL = 8 × 2 = 16,

gM = 20 − 16 = 4.

The electronic configuration is σ2 π1x π1y , indicating a Mo=Mo double bond. The experimental bond distance is 252.3 pm, and the molecule is a paramagnetic species. 19.2.4

Quintuple bonding in a dimetal complex

Recently, structural evidence for the first quintuple bond between two metal atoms was found in the dichromium(I) complex Ar, CrCrAr, (where Ar, is the sterically encumbering monovalent 2,6-bis[(2,6-diisopropyl)phenyl]phenyl ligand). This complex exists as air- and moisture-sensitive dark-red crystals that remain stable up to 200◦ C. X-ray diffraction revealed a centrosymmetric molecule with a planar trans-bent C–Cr–Cr–C backbone with measured structural parameters Cr–Cr 183.51(4) pm, Cr–C 213.1(1) pm, and C–Cr–Cr 102.78(3)◦ . Characterization of the compound is further substantiated by magnetic and spectroscopic data, as well as theoretical computations. Figure 19.2.6 shows the molecular geometry and structural formula of Ar, CrCrAr, . In principle, a homodinuclear transition-metal species can form up to six bonds using the ns and five (n-1)d valence orbitals. In a simplified bonding description of Ar, CrCrAr, , the planar C–Cr–Cr–C skeleton has idealized molecular symmetry C2h with reference to a conventional z axis lying perpendicular to it. For each chromium atom, a local z axis is chosen to be directed toward

Metal–Metal Bonds i

i i

i

Pr i

i

Pr

Pr

Cr

Cr

Pr

Pr

713

i i

Pr

Pr

Pr

the other chromium atom, and the local x axis to lie in the skeletal plane. Each chromium atom (electronic configuration 3d5 4s1 ) uses it 4s orbital to overlap with a sp2 hybrid orbital on the ipso carbon atom of the terphenyl ligand to form a Cr–C σ bond. That leaves five d orbitals at each Cr(I) center for the formation of a fivefold (i.e., quintuple) metal–metal bond, which has one σ (dz2 + dz2 ; symmetry species Ag ), two π (dyz + dyz , dxz + dxz ; Au , Bu ) and two δ (dx2 −y2 + dx2 −y2 , dxy + dxy ; Ag , Bg ) components. The situation is actually more complex as mixing of the chromium 4s, 3dz2 and 3dx2 −y2 orbitals (all belonging to Ag ) can occur. In an alternative bonding scheme, each chromium atom may be considered to be dz2 s hybridized. The outward-extended (s − dz2 ) hybrid orbital is used to form a Cr–C σ bond. Note that this type of overlap results in a C–Cr–Cr angle of 90◦ and allows free rotation of the C–Cr bond about the Cr–Cr axis, and it is the steric repulsion between the pair of bulky Ar, ligands that accounts for the obtuse C–Cr–Cr bond angle and the trans-bent geometry of the central C–Cr–Cr–C core. The pair of chromium (s + dz2 ) hybrid orbitals aligned along the common local z axis overlap to form the metal–metal σ bond, while the π and δ bonds are formed in the manner described above. In either bonding description, there is a formal bond order of 5 between the chromium(I) centers.

19.3

Clusters with three or four transition-metal atoms

19.3.1

Trinuclear clusters

Table 19.3.1 lists the structural data and bond valences of some trinuclear clusters. In Os3 (CO)9 (µ3 -S)2 , the Os3 unit is in a bent configuration with two Os–Os bonds of average length 281.3 pm, and the other Os· · · Os distance (366.2 pm) is significantly longer. The cluster (CO)5 Mn–Fe(CO)4 –Mn(CO)5 adopts a linear configuration. The other clusters are all triangular. The Fe3 skeleton of Fe3 (CO)12 has 48 valence electrons, and the Fe3 unit contains three Fe–Fe single bonds. The Os3 skeleton of Os3 H2 (CO)10 , a 46-electron triangular cluster, has one Os=Os double bond and two Os–Os single bonds. The length of the Os=Os double bond is 268.0 pm, and the Os–Os single bonds are 281.8 and 281.2 pm. The remaining three clusters [Mo3 (µ3 -S)2 (µ2 -Cl)3 Cl6 ]3− , [Mo3 (µ3 -O) (µ2 -O)3 F9 ]5− , and Re3 (µ2 -Cl)3 (CH2 SiMe3 )6 all have nearly equilateral M3 skeletons. According to the calculated bond valences of 5, 6, and 9 for the

Fig. 19.2.6.

Molecular geometry and structural formula of the dinuclear complex Ar, CrCrAr, (Ar, = C6 H3 -2,6(C6 H3 -2,6-i Pr2 )2 .

714

Structural Chemistry of Selected Elements Table 19.3.1. Some trinuclear clusters

Cluster

g

b

Os3 (CO)9 (µ3 -S)2 Mn2 Fe(CO)14 Fe3 (CO)12 Os3 H2 (CO)10

50 50 48 46

2 2 3 4

[Mo3 (µ3 -S)2 (µ2 -Cl)3 Cl6 ]3− [Mo3 (µ3 -O)(µ2 -O)3 F9 ]5− Re3 (µ2 -Cl)3 (CH2 SiMe3 )6 Os Fe Mn Fe Mn Os Os Fe (a) ∗

(b)

44 42 36

M–M(pm)

Figure

Os–Os, 281.3 Mn–Fe, 281.5 Fe–Fe, 281.5 two Os–Os, 281.5 Os=Os, 268.0 5 Mo- - -Mo, 261.7∗ 6 Mo=Mo, 250.2 9 Re≡Re, 238.7 Mo Os Os Mo

Fe Os

(c)

(d)

(a) (b) (c) (d) (e) (f) (g) Mo Mo Re

Mo Mo (e)

Re

(f)

Re (g)

Bond order of 1 23 .

Table 19.3.2. Some tetranuclear clusters

Cluster

g

b

M–M(pm)

Figure

Re4 (µ3 -H)4 (CO)12 Ir4 (CO)12 Re4 (CO)16 2− Fe4 (CO)13 C Co4 (CO)10 (µ4 -S)2 Re4 H4 (CO)15 2− Co4 (µ4 -Te)2 (CO)11 Co4 (CO)4 (µ-SEt)8

56 60 62 62 64 64 66 68

8 6 5 5 4 4 3 2

6 Re- - -Re, 291∗ 6 Ir–Ir, 268 5 Re–Re, 299 5 Fe–Fe, 263 4 Co–Co, 254 4 Re–Re, 302 3 Co–Co, 262 2 Co–Co, 250

(a) (b) (c) (d) (e) (f) (g) (h)

(a) ∗

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Bond order of 1 13 .

metal–metal bonds in these compounds, the bond types are Mo- - -Mo (bond order 1 23 ), Mo=Mo, and Re≡Re, respectively. 19.3.2

Tetranuclear clusters

Table 19.3.2 lists the bond valence and structural data of some tetranuclear clusters. The bond valence of Re4 (µ3 -H)4 (CO)12 is 8, and the tetrahedral Re4 skeleton can be described in two ways: (I) resonance between valence-bond structures, leading to a formal bond order of 1 13 , and (II) four 3c-2e ReReRe bonds. Since there are already four µ3 -H capping the faces, description (II) is not as good as (I).

Metal–Metal Bonds

(I)

1 (II)

4

1

2

4

1

2

2

4

3 3

3

In other examples listed in Table 19.3.2, the calculated bond valence b is just equal to the number of edges of the corresponding metal skeleton, signifying 2c-2e M–M single bonds. 19.4

Clusters with more than four transition-metal atoms

19.4.1

Pentanuclear clusters

Selected examples of pentanuclear metal clusters are listed in Table 19.4.1. In these examples, the calculated bond valence b is exactly the same as the number of edges of the metal skeleton, indicating 2c-2e M–M bonds. In general, electron-rich species have lower bond valence and more open structures than the electron-deficient ones. The structures and skeletal bond valences of Os5 (CO)16 and B5 H5 2− are similar as a pair, as are also Fe5 C(CO)15 and B5 H9 . But the bonding types in the boranes and the metal clusters are not the same. Since every B atom in a polyhedral borane has three AO’s for bonding of the Bn skeleton, any vertex more than three-connected must involve multicenter bonds. In the transition-metal skeleton, the Mn atoms form either 2c-2e single bonds or 3c-2e multicenter bonds. Some clusters have 76 valence electrons based on a trigonal bipyramidal skeleton, such as [Ni5 (CO)12 ]2− , [Ni3 Mo2 (CO)16 ]2− , Co5 (CO)11 (PMe2 )3 , and [FeRh4 (CO)15 ]2− , which are not shown in Table 19.4.1. The additional four valence electrons compared to Os5 (CO)16 have a significant effect on its geometry, and the bond lengths to the apical metal atoms are increased, and the bond valence b is decreased. The cluster [Os5 C(CO)14 (O2 CMe)I] has 78 valence electrons, which is not shown in Table 19.4.1, and its bond valence is equal to 6: [b = 12 (5×18−78) = 6]. This cluster has a deformed trigonal bipyramidal geometry with no bonding in the equatorial plane of the bipyramid. 19.4.2

Hexanuclear clusters

Table 19.4.2 lists the bond valence and structural data of some selected examples of hexanuclear clusters. The first three clusters have different b values, yet they

715

716

Structural Chemistry of Selected Elements Table 19.4.1. Some pentanuclear clusters

Cluster

g

b

No. of edges

Figure

Os5 (CO)16 Fe5 C(CO)15 Os5 H2 (CO)16 Ru5 C(CO)15 H2 Os5 (CO)18 Os5 (CO)19 Re2 Os3 H2 (CO)20

72 74 74 76 76 78 80

9 8 8 7 7 6 5

9 8 8 7 7 6 5

(a) (b) (c) (d) (e) (f) (g)

(a)

(b)

(c)

(d)

(e)

(f)

(g)

are all octahedral with 12 edges. There are three stable types of bonding schemes for an octahedron, as shown in Fig. 19.1.2: (a) Mo6 Cl14 2− , g = 84, b = 12; in this cluster there are 12 2c-2e bonds at the 12 edges. (b) Nb6 Cl18 4− , g = 76, b = 16; in this cluster there are eight 3c-2e bonds on the eight faces of an octahedron. (c) Rh6 (CO)16 , g = 86, b = 11; in this cluster there are four 3c-2e bonds on four faces and three 2c-2e bonds at three edges, as in the case of B6 H2− 6 .

Table 19.4.2. Some hexanuclear clusters

Cluster

g

b

No. of edges

Figure

Mo6 (µ3 -Cl)8 Cl2− 6 Nb6 (µ2 -Cl)12 Cl4− 6 Rh6 (CO)16 Os6 (CO)18 Os6 (CO)18 H2 Os6 C(CO)16 (MeC≡CMe) Ru6 C(CO)2− 15 Os6 (CO)20 [P(OMe)3 ] Co6 (µ2 -C2 )(µ4 -S)(CO)14

84 76 86 84 86 88 90 90 92

12 16 11 12 11 10 9 9 8

12 12 12 12 11 10 9 9 8

(a) (a) (a) (b) (c) (d) (e) (f) (g)

(a)

(b)

(c)

(d)

(e)

(f)

(g)

Other clusters listed in Table 19.4.2 have the property that their b value equals the number of edges of their Mn skeletons.

Metal–Metal Bonds 19.4.3

717

Clusters with seven or more transition-metal atoms

Table 19.4.3 listed the bond valence and structural data of some selected examples of high-nuclearity clusters, each consisting of seven or more transition-metal atoms. The skeletal structures of these clusters are shown in Fig. 19.4.1. Table 19.4.3. Clusters with more than six transition metal atoms

Cluster

g

b

Structure (Fig. 19.4.1)

Os7 (CO)21 [Os8 (CO)22 ]2− [Rh9 P(CO)21 ] 2−

98 110 130

14 17 16

(a) (b) (c)

[Rh10 P(CO)22 ]−

142

19

(d)

[Rh11 (CO)23 ]3− [Rh12 Sb(CO)27 ]3−

148 170

25 23

(e) (f)

Remark

Capped octahedron Para-bicapped octahedron Capped square antiprism; iso-bond valence with B9 H13 Bicapped square antiprism; iso-bond valence with B10 H2− 10 Three face-sharing octahedra Icosahedron; iso-bond valence with B12 H2− 12

When the number of metal atoms in a cluster increases, the geometries of the clusters become more complex, and some are often structurally better described in terms of capped or decapped polyhedra and condensed polyhedra. For example, the first and second clusters listed in Table 19.4.3 are a capped octahedron and a bicapped octahedron, respectively. Consequently, capping or decapping with a transition-metal fragment to a deltapolyhedral cluster leads to an increase or decrease in the cluster valence electron count of 12. When a transition-metal atom caps a triangular face of the cluster, it forms three M–M bonds with the vertex atoms, so according to the 18-electron rule, the cluster needs an additional 18 − 6 = 12 electrons. The parent octahedron of [Os6 (CO)18 ]2− has g = 86, the monocapped octahedron Os7 (CO)21 has g = 98, and the bicapped octahedron [Os8 (CO)22 ]2− has g = 110. (a)

(b)

(c)

(d)

(e)

(f) Fig. 19.4.1.

Structures of some transition-metal clusters: (a) Os7 (CO)21 , (b) [Os8 (CO)22 ]2− , (c) [Rh9 P(CO)21 ]2− , (d) [Rh10 P(CO)22 ]− , (e) [Rh11 (CO)23 ]3− , and (f) [Rh12 Sb(CO)27 ]3− .

718

Structural Chemistry of Selected Elements The metal cluster of [Rh10 P(CO)22 ]− forms a deltapolyhedron, which has g = 142, as shown in Fig. 19.4.1(d). The skeleton of [Rh9 P(CO)21 ]2− is obtained by removal of a vertex transition-metal fragment. The skeletal valence electron count of [Rh9 P(CO)21 ]2− gives g = 142 − 12 = 130. The metal cluster of [Rh11 (CO)23 ]3− is composed of three face-sharing octahedra, as shown in Fig. 19.4.1(e). The metal cluster of [Rh12 Sb(CO)27 ]3− consists of an icosahedron with an encapsulated Sb atom at its center. Generally, capped or decapped deltapolyhedral clusters are characterized by the number of skeletal valence electrons g g = (14n + 2) ± 12m, where n is the number of M atoms in the parent deltapolyhedron and m is the number of capped (+) or decapped (−) metal fragments. A classical example of correlation of structure with valence electron count of transition-metal clusters is shown in Fig. 19.4.2. There the structures of a series of osmium clusters are systematized by applying the capping and decapping procedures. 19.4.4

Anionic carbonyl clusters with interstitial main-group atoms

There is much interest in transition-metal carbonyl clusters containing interstitial (or semi-interstitial) atoms in view of the fact that insertion of the encapsulated atom inside the metallic cage increases the number of valence electrons but leaves the molecular geometry essentially unperturbed. The clusters are generally anionic, and the most common interstitial heteroatoms are carbon, nitrogen, and phosphorus. Some representative examples are displayed in Fig. 19.4.3. The core of the anionic carbonyl cluster [Co6 Ni2 (C)2 (CO)16 ]2− consists of two trigonal prisms sharing a rectangular face [Fig. 19.4.3(a)]. All four vertical edges and two horizontal edges, one on the top face and the other on the bottom face, are each bridged by a carbonyl group. Each of the two Co∗ atoms has two terminal carbonyl groups, and each of the Ni and Co atoms has one. The [Os18 Hg3 (C)2 (CO)42 ]2− cluster is composed of two tricapped octahedral Os9 (C)(CO)21 units sandwiching a Hg3 triangle (Fig. 19.4.3(b)). Each corner Os atom in the top and bottom faces has three terminal carbonyl groups, and the remaining Os atoms each have two. The core of the [Fe6 Ni6 (N)2 (CO)24 ]2− cluster comprises a central Ni6 octahedron that shares a pair of opposite faces with two Ni3 Fe3 octahedra, as shown in Fig. 19.4.3(c). The interstitial N atoms occupy the centers of the Ni3 Fe3 octahedra. Each Fe atom has two terminal carbonyl groups, and each Ni atom has one. The metallic core of the [Rh28 (N)4 (CO)41 Hx ]4− cluster is composed of three layers of Rh atoms in a close-packed ABC sequence, as shown in Fig. 19.4.3(d). Four N and an unknown number of H atoms occupy the octahedral holes. The metal atoms in [Ru8 (P)(CO)22 ]− constitute a square antiprismatic assembly [Fig. 19.4.3(e)]. Two opposite slant edges are each bridged by a carbonyl group. Each Ru bridged atoms has two terminal carbonyl groups, and each

Metal–Metal Bonds closo-

–12e

–12e

nido-

719

arachno-

octahedron [Os6(CO)21]2– 86e

+ 12e

[Os5C(CO)15 74e

[Os4N(CO)12]– 62e

monocapped Os7(CO)21 98e

H2Os5(CO)16 74e

H2Os6(CO)18 86e

+ 12e

bicapped

[Os8(CO)22] 110e

(98e)

Os6(CO)18(py) 86e

(110e)

Os7H2(CO)20 98e

+ 12e

tricapped (122e)

+ 12e

tetracapped

Fig. 19.4.2. 2–

Os10C(CO)24 134e

5–

[Os9(CO)21R] 120e or 122e

[Os8H(CO)22]– 110e

of the remaining four has three. Comparison of this cluster core with those of [Rh9 (P)(CO)21 ]2− [Fig. 19.4.3(f)] and [Rh10 (S)(CO)22 ]2− [Fig. 19.4.3(g)] shows that the latter two are derived from successive capping of the rectangular faces of the square antiprism.

19.5

Iso-bond valence and iso-structural series

For a cluster consisting of n1 transition-metal atoms and n2 main-group atoms, the bond valence b is evaluated as b = 12 (18n1 + 8n2 − g),

The structures of osmium carbonyl compounds vary with an increase or decrease of the valence electrons.

720

Structural Chemistry of Selected Elements (a)

(b)

Os Os

Os

Os

Os

Os

Os

Os Os

Co

Co

Ni

Co*

Hg

Hg

Hg Co*

Ni

Os

Co

Co

Os

Os

Os Os (c)

Os Os

(d) Fe Fe

Ni Ni Ni

Ni

Fe

C

B

Fe

A C

Fe (e)

A

(f)

B

Ru

Ru

Ru

Rh

Ru

Ru

B

B

C

(g) Rh

Rh

Ru Ru

C A C

B

Rh

Ru

B

A C

B

C

B

C

B

A

Ni

B

A C

B

Ni

Os

C

B

Fe

Os

Rh Rh Rh

Rh Rh

Rh

Rh Rh

Rh Rh Rh

Rh Rh

Rh

Rh Fig. 19.4.3.

Molecular structure of some carbonyl cluster anions containing encapsulated heteroatoms; all terminal CO groups are omitted for clarity; (a) [Co6 Ni2 (C)2 (CO)16 ]2− ; only the bridging CO groups are shown; (b) [Os18 Hg3 (C)2 (CO)42 ]2− ; (c) [Fe6 Ni6 (N)2 (CO)24 ]2− ; (d) [Rh28 (N)4 (CO)41 Hx ]4− ; to avoid clutter, not all Rh–Rh bonds are included; (e) [Ru8 (P)(CO)22 ]− ; (f) [Rh9 (P)(CO)21 ]2− ; (g) [Rh10 (S)(CO)22 ]2− .

where g is the number of valence electrons of the skeleton formed by the n1 transition-metals and n2 main-group atoms. + When a BH group of the octahedral cluster (BH)2− 6 is replaced by a CH group, both g and b retain their values and the structure of the cluster anion (BH)5 CH− remains octahedral. On the other hand, when a BH group of (BH)2− 6 is replaced by a Ru(CO)3 group, the b value still remains the same. But g

Metal–Metal Bonds

721

CH BH 2–

(BH)6 g = 26, b = 11

Ru(CO)3 (BH)4(CH)2 g = 26, b = 11

[Ru(CO)3]4(CH)2 g = 66, b = 11

Fig. 19.5.1.

Iso-bond valence and iso-structural series of B6 H2− 6 .

increases its value by 10, as a BH group contributes 4 electrons to the skeleton, while a Ru(CO)3 group contributes 14 (8 from Ru and 2 from each CO). + Therefore, replacement of one or more BH groups in (BH)2− 6 by either CH or Ru(CO)3 groups results in a series of iso-bond valence and iso-structural clusters. The structures of some members of this series, (BH)2− 6 , (BH)4 (CH)2 , 2− [Ru(CO)3 ]4 (CH)2 , and [Ru(CO)3 ]6 , are shown in Fig. 19.5.1. Similar substitutions by either transition-metal or representative-element groups give rise to a variety of cluster compounds, and five iso-structural series of clusters containing both transition-metal and main-group element components are displayed in Fig. 19.5.2. Clearly the structure of a given cluster depends on electronic, geometric, and other factors. Hence the structure of a compound cannot be predicted until it has been determined experimentally. Still, based on the bond valence and structural principle illustrated above, an educated guess on the structure of a cluster becomes feasible. In addition, the bond valence concept provides a useful link between apparently dissimilar clusters such as (BH)2− 6 and [Ru(CO)3 ]4 (CH)2 . 19.6

Selected topics in metal–metal interactions

Since the 1980s, studies on metal clusters and metal string complexes have revealed unusual interactions between metal atoms, some of which are discussed in this section. 19.6.1

Aurophilicity

The term aurophilicity (or aurophilic attraction) refers to the formally nonbonding but attractive interaction between gold(I) atoms in gold cluster compounds. The Au(I) atom has a closed-shell electronic configuration: [Xe] 4f14 5d10 6s0 . Normally, repulsion exists between the nonbonding homoatoms. However, there is extensive crystallographic evidence of attractive interaction between gold(I) cations. Figure 19.6.1 shows the structures of three Au(I) compounds. (1) O[AuP(o-tol)3 ]+ 3 (o-tol = C6 H4 Me-2): In O[AuP(o-tol)3 ]3 (BF4 ), the O atom forms covalent bonds with three Au atoms in a OAu3 pyramidal configuration, as shown in Fig. 19.6.1(a). The Au atoms are linearly

[Ru(CO)3]62– g = 86, b = 11

722

Structural Chemistry of Selected Elements b=5

g=

Fe4(CO)13H– 62

OS3(SEt)(CO)10H 52

Fe2(SR)2(CO)6 42

Ir4(CO)12 60

Co3(CO)9(CR) 50

Co2(CO)6(CR)2 40

Fe5C(CO)15 74

Fe3(CO)9S2 54

Mn(CO)4B3H8 32

B4H10 22

b=6

g=

Co(CO)3(CR)3 30

(CR)4 20

CoCpB4H8 34

B5H9 24

b=8

g=

Fe2(CO)6B3H7 44

b=9

g=

Os4S(CO)12 62

Os5(CO)16 72

P3[Co(triphos)]3+ 2 42

Fe3As2(CO)9 52

C2B3H5 22

b = 11

Rh6(CO)16 g=

86

Os5S(CO)15 76

Fe4(PPh)2 (CO)11 66

Co3Cp3B3H5 56

Co2Cp2B4H5 46

Fe(CO)3 B5H3(CO)2 36

C2B4H6 26

Fig. 19.5.2.

Iso-structural series of transition-metal and main-group clusters.

coordinated by O and P atoms. In this structure, the mean Au· · · Au distance is 308.6 pm, which is shorter than the sum of van der Waals radii, 2 × 166 = 332 pm. (2) S[AuP(o-tol)3 ]2+ 4 : In S[AuP(o-tol)3 ]4 (ClO4 )2 , the SAu4 unit takes a squarepyramidal configuration, as shown in Fig. 19.6.1(b). The Au atoms are near linearly coordinated by S and P atoms. The Au· · · Au distances lie in the range of 288.3 to 293.8 pm, and the mean distance is 293.0 pm. The distance of the S atom to the center of the Au4 basal plane is 130 pm. (3) Au11 I3 [P(p-C6 FH4 )3 ]7 : The structure of the molecule is shown in Fig. 19.6.1(c). In the Au11 cluster, the central Au atom is surrounded by ten Au atoms, which form an incomplete icosahedron (lacking two vertices) with each vertex carrying one terminal iodo ligand or P(p-C6 FH4 )3 group.

Metal–Metal Bonds (a)

723

(b)

O

S Au

Au P

P

(c)

P Au

I Fig. 19.6.1.

Molecular structure of gold cluster compounds: (a) O[AuP(o-tol)3 ]+ 3 , (b)

S[AuP(o-tol)3 ]2+ 4 , (c) Au11 I3 [P(p-C6 FH4 )3 ]7 .

The mean Au· · · Au distance from the central atom to the surrounding atoms is 268 pm, and the mean distance between the ten Au vertices is 298 pm. In other gold(I) cluster compounds, such as tetrahedral [(AuL)4 (µ4 -N)] and [(AuL)4 (µ4 -O)]2+ , trigonal-bipyramidal [(AuL)5 (µ5 -C)]+ , [(AuL)5 (µ5 N)]2+ and [(AuL)5 (µ5 -P)]2+ , and octahedral [(AuL)6 (µ6 -C)]2+ and [(AuL)6 (µ6 -N)]3+ (L = PPh3 or PR3 ), the Au· · · Au distances lie in the range 270 to 330 pm. These data substantiate that aurophilicity is a common phenomenon among gold cluster complexes. (c)

Cl

Au Au mes

O Au

N

Aurophilicity presumably arises from relativistic modification of the gold valence AOs energies, which brings the 5d and 6s orbitals into close proximity in the energy level diagram. In more recent theoretical studies, the effect is primarily attributed to electron correlation, which takes precedence over 6s/5d hybridization. To date, the origin of the aurophilicity has not yet been unambiguously established. Making use of the concept of aurophilicity, simple gold compounds can be combined to yield complicated oligomeric aggregates in designed synthesis. Figure 19.6.2 shows the structures of three oligomeric molecules.

Fig. 19.6.2.

Structure of some gold oligomeric aggregate molecules: (a) Au5 (mes)5 (mes = C6 H3 Me3 -2,4,6); (b) [LAuCl]4 ,

--

(b)

--

(a)

L = HN(CH2 )4 CH2 ; and (c) [O(AuPPh3 )3 ]2 .

724

Structural Chemistry of Selected Elements (a)

(b) L

R

(c) L’

R’

R

Ag

Ag Fig. 19.6.3.

Some mixed Au and Ag metal complexes (filled circle, Au; open circle, Ag): (a) [Au(CH2 PPh2 )2 ]2 [Ag(OClO3 )2 ]2 , (b) [Au(C6 F5 )]2 [Ag(C6 H6 )]2 , and (c) [Au(C6 F5 )]2 [Ag(COMe2 )]2 .

L

L

Au

R

R

L’

R’

L’’ R’’

Ag

Au

R’ L’

L

19.6.2

L’

R’

R’’ Au

R’’

R’’ L’’

Argentophilicity and mixed metal complexes

By analogy to aurophilicity, argentophilicity has been demonstrated to exist in silver cluster complexes. In the crystal structures of a variety of silver(I) double and multiple salts containing a fully encapsulated acetylide dianion C2− 2 (IUPAC name acetylenediide) in different polyhedral silver cages (see Fig. 14.3.11), there exist many Ag· · · Ag contacts shorter than twice the van der Waals radius of silver (2 × 170 = 340 pm). Further details are given in Chapter 20. Taking advantage of both aurophilicity and argentophilicity, tetranuclear mixed-metal complexes which contain pairs of Au and Ag atoms have been prepared, as shown in Fig. 19.6.3. In the preparation of mixed gold/silver polynuclear complexes, aurophilicity and argentophilicity have been utilized to promote cluster formation. Figure 19.6.4 shows the cores of several mixed gold-silver clusters. The [Au13Ag12 ] molecular skeletons (a) and (b) of [(Ph3 P)10Au13Ag12 Br8 ] SbF6 and [(p-tol3 P)10Au13Ag12 Br8 ]Br, respectively, can each be considered as two centered icosahedra sharing a common vertex. In an alternative description, the 25 metal atoms constitute three fused icosahedra, with a common pentagon shared between an adjacent pair of fused icosahedra. Structure (a) adopts the ses (staggered-eclipsed-staggered) configuration, and the sequence of relative positioning of atoms isABBA. Structure (b) adopts the sss (staggeredstaggered-staggered) configuration, and the sequence is ABAB. The structure of (c) consists of the three centered icosahedra, each of which uses one edge to form a central triangle, with an additional Ag atom lying above and below it. The structure of (d) consists of six Au atoms that form a planar six-membered ring, with one Ag atom located at the center; each edge of the Au6 hexagon is bridged by a bridging C atom, with three C atoms lying above the plane and three below it. 19.6.3

Metal string molecules

A metal string molecule contains a linear metal-atom chain in its structure. In a molecule of this type, all or a part of the neighboring metal atoms are involved in metal–metal bonding interactions. A general strategy of synthesizing metal string molecules is to design bridging ligands possessing multiple donor sites arranged in a linear sequence such that they can coordinate simultaneously to metal centers.

Metal–Metal Bonds (a)

725

(b) B

A s

s

B

A e

s

B

B s

s

A

A

(c)

(d)

Fig. 19.6.4.

Skeletal structure of some mixed Au/Ag clusters (filled circle, Au; open circle, Ag): (a) [Au13Ag12 ] in [(Ph3 P)10Au13Ag12 Br8 ]SbF6 , (b) [Au13Ag12 ] in [(p-tol3 P)10Au13Ag12 Br8 ]Br, (c) [Au18Ag20 ] in [(p-tol3 P)12Au18Ag20 Cl14 ], and (d) [AgAu6 C6 ] in [Ag(AuC6 H2 (CHMe2 )3 )6 CF3 SO3 .

(1)

Metal string molecules constructed with oligo(α-pyridyl)amido ligand The common formula of a series of polypyridylamines is shown below: n = 0, Hdpa n = 1, H2tpda N

N

N

N

n = 2, H3teptra

N

n = 3, H4peptea

H n

H

Four fully deprotonated polypyridylamines, or oligo(α-pyridyl)amido ligands, can coordinate simultaneously to metal atoms from the upper, lower, front, and back directions to form a metal string molecule:

N X M

N M

N M

N M

n

4 N M X

n 0 1 2 3

M (II) Cr, Ru, Co, Rh, Ni, Cu Cr, Co, Ni Cr, Ni Cr, Ni

As an oligo(α-pyridyl)amido ligand has an odd number of donor sites, the corresponding metal string molecule has the same number of metal atoms. From the reactions of Ni(II) salts with polypyridylamines, a series of metal string molecules, in which the number of nickel atom varies from 3 (i.e., n =

726

Structural Chemistry of Selected Elements 0) to 9 (i.e., n = 3), have been prepared. The structures of these molecules are very similar. Figure 19.6.5 shows the structure of [Ni9 (µ9 -peptea)4 Cl2 ], (H4 peptea = pentapyridyltetramine). The nine Ni atoms are in a straight line, and the distances between atoms are approximately equal. Every N atom in the four (α-pyridyl)amido ligands coordinates to one Ni atom. Each Ni atom is coordinated by four N atoms to form a square oriented perpendicular to the metal string. Because of steric repulsion between H atoms of the neighboring pyridine rings, the (α-pyridyl)amido ligands are helically distributed around the string axis, as shown in Fig. 19.6.5.

Fig. 19.6.5.

Structure of [Ni9 (µ9 -peptea)4 Cl2 ] (filled circle, Ni; large open circle, Cl; small open circle, N; and small filled circle, C).

The Ni–Ni and Ni–N distances in a family of related metal string molecules, in which the numbers of Ni atoms are 3, 5, 7, and 9, are shown in Fig. 19.6.6. The Ni–Ni distances increase from the center toward each terminal, and the Ni–N distances are nearly equal except for the outermost ones. These effects (a)

(b) 189

210

190

244.3

190

211

230.5

238.3

(c) 193 237.9

230.7

229.9

225.4

193

190

211

222.0

(d) 193 238.6

192

192

192

211

224.0

Fig. 19.6.6.

Bond lengths in metal string molecules (in pm): (a) Ni3 (µ3 -dpa)4 Cl2 , (b) Ni5 (µ5 -tpda)4 Cl2 , (c) Ni7 (µ7 -teptra)4 Cl2 , and (d) Ni9 (µ9 -peptea)4 Cl2 .

Metal–Metal Bonds

727

are attributable to the fact that, unlike the inner metal atoms, each terminal metal atom has square-pyramidal coordination. The metal string molecule [Cr5 (tpda)4 Cl2 ]· 2Et2 O·4CHCl3 contains alternately long and short metal–metal distances, as shown in Fig. 19.6.7. The short Cr–Cr distances are 187.2 and 196.3 pm, which correspond to the quadruple bond Cr= =Cr. The long Cr· · · Cr distances are 259.8 and 260.9 pm, which are indicative of nonbonding interaction. Fig. 19.6.7.

196.3

260.9

187.2

Structure of Cr5 (tpda)4 Cl2 (bond length in pm) (large filled circle, Cr; small filled circle, C; large open circle, Cl; small open circle, N).

259.8

(2) Hexanuclear metal string cationic complexes Modification of the H2 tpda ligand by substitution of the central pyridyl group with a naphthyridyl group gives rise to the new ligand 2,7-bis (α-pyridylamino)-1,8-naphthyridine (H2 bpyany), which has been used to generate a series of hexanuclear metal string complexes of the general formula [M6 (µ6 -bpyany)4 X2 ]Yn (M=Co, Ni; X− = terminal monoanionic ligand; Y− = counter monoanion; n = 1, 2). All compounds contain a linear hexanuclear cation helically supported by four bpyany2− ligands and conforms approximately to idealized D4 molecular symmetry if the axial terminal ligands are ignored. The structure of a representative example is shown in Fig. 19.6.8.

N

N H

N

N

N H

N

Fig. 19.6.8.

Structural formula of the H2 bpyany ligand and molecular geometry of the hexanuclear monocation in crystalline [Co6 (µ6 -bpyany)4 Cl2 ]PF6 .

H2bpyany

The averaged metal–metal bond lengths in the series of linear M12+ 6 (M = Co, Ni) complexes and their M11+ one-electron reduction products are 6 Table 19.6.1. Hexanuclear metal string complexes and average M–M bond distances

M

X

Y

n

Bond distance (pm) averaged for D4 symmetry Outermost Mid-way Innermost

Co Co Co Co Ni Ni

NCS NCS CF3 SO3 CF3 SO3 NCS Cl

PF6 PF6 CF3 SO3 CF3 SO3 BPh4 PF6

2 1 2 1 2 1

231.3(1) 231.3(1) 228.3(1) 228.4(1) 240.3(1) 241.1(3)

225.5(1) 227.3(1) 224.3(1) 224.9(1) 231.4(1) 228.5(3)

224.5(1) 225.6(1) 226.7(1) 225.1(1) 229.6(1) 220.2(3)

728

Structural Chemistry of Selected Elements tabulated in Table 19.6.1. In all complexes the outermost M–M distance is in general slightly longer than the inner bond distances, but neither the nature of system results the axial ligands nor the addition of one electron to the Co12+ 6 in significant structural changes. In contrast, the innermost Ni–Ni bond shows a substantial decrease of 9.4(3) pm upon one-electron reduction of the Ni12+ 6 system. The crystallographic data are consistent with the proposed model of a delocalized electronic structure for the Con+ 6 (n = 11, 12) complexes, whereas 12+ the extra electron in the Ni6 system partakes in a δ bond constructed from dx2 −y2 orbitals of the naphthyridyl-coordinated nickel atoms. (3) Mixed-valence metal string complexes of gold The structures of two gold metal string molecules are shown in Fig. 19.6.9. The formula of molecule (a) in this figure is: Ph2 P Au

R

R

Ph2 P

R

(AuR4)–, R = C6F5

Au R

Au Au Au

P Ph2

+

P Ph2

From the Au–Au bond lengths shown and related theoretical calculations, the valence states of the Au atoms are in the sequence of Au(III)–Au(I)–Au(I)–Au(I)–Au(III). The molecular cation is composed of the central unit [Au(C6 F5 )2 ]− and two outer dinuclear gold cations [Au2 {(CH2 )2 (PPh2 )}2 C6 F5 ]+ , with the central unit donating electrons to the outer units. The formula of molecule (b) in Fig. 19.6.9 is Ph2 P R

Au

Au

P Ph2

Ph2 P Au

Au

P Ph2

Ph2 P Au

2+

(ClO4–)2, R = C6F3H2

Au R

P Ph2

(a)

275.5

264.0

(b) Fig. 19.6.9.

Structures of two mixed-valence metal string molecules (large filled circle, Au; large open circle, R group; small filled circle, C; small open circle, P; bond lengths in pm).

283.8

273.7

265.4

Metal–Metal Bonds

729

From theAu–Au bond lengths shown and theoretical calculations, the valence states of the Au atoms are identified as Au(III)–Au(I)–Au(I)–Au(I)–Au(I)– Au(III).

Rh N Fig. 19.6.10.

C

19.6.4

Structure of a section of the infinite ]∞ . rhodium chain, [Rh(CH3 CN)1.5+ 4

Metal-based infinite chains and networks

Infinite metal-based chains are expected to be much more promising as conducting inorganic “molecular wires” than short-chain oligomers. The infinite rhodium chain, [Rh(CH3 CN)1.5+ ]∞ , consists of alternating Rh–Rh distances of 4 284.42 and 292.77 pm, and is a semiconductor. Figure 19.6.10 shows a section of the infinite cationic chain in the polymer [{Rh(CH3 CN)4 }(BF4 )1.5 ]∞ . A series of polymeric complexes featuring the metallophilic interaction between gold(I) and thallium(I) has been synthesized employing acid–base strategy. For example, the treatment of Bu4 N[Au(C6 Cl5 )2 ] with TlPF6 in THF gave [AuTl(C6 Cl5 )2 ]n , which consists of an infinite linear (Tl· · · Au· · · )∞ chain consolidated by unsupported AuI · · · TlI interactions, as shown in Fig. 19.6.11(a). In the presence of triphenylphosphine oxide, and also depending on the nature of the pentahalophenyl group employed, similar synthetic reactions afforded [AuTl(C6 F5 )2 (Ph3 P=O)2 ]n and [AuTl(C6 Cl5 )2 (Ph3 P=O)2 (THF)]n with the Cl

(a)

Cl

(b)

Cl

Cl

Cl

Cl

Cl

Cl

Cl

Cl

Au Cl

300.44pm

Cl

Cl

Cl Cl

Tl

297.26 Au Cl

F

Cl

F

F Tl

Cl Cl Cl

Fig. 19.6.11.

Structure of (a) [AuTl(C6 Cl5 )2 ]n and (b) [AuTl(C6 F5 )2 (Ph3 P=O)2 ]n .

F

F F O

F Au

F

F

Ph3P

308.62 pm Tl O

F

Ph3P F 303.58 Au

Tl F

F

Ph3P F

F F

O

F

O Ph3P

F

F F

730

Structural Chemistry of Selected Elements Cl

Cl O PPh3 Cl

THF

Cl

Tl'

314.52 Au 316.30

Cl

Cl

Cl

Cl

305.29pm

332.05

Cl

Cl Au

Tl

Cl Cl

Cl

Cl

Cl

Cl Cl

Ph3P O Cl

Cl

Cl

Cl

Cl

Au

Cl

Ph3P O Cl

Cl

Cl

Tl

Tl'

Cl

Cl

O PPh3 Cl

THF

Cl

Cl

Cl

Cl

Cl

Cl Au Cl

Cl

Cl

Cl

Cl

Fig. 19.6.12.

Structure of [AuTl(C6 Cl5 )2 (Ph3 P=O)2 (THF)]n .

phosphine oxide incorporated into their polymeric structures. In the pentafluorophenyl complex, thallium(I) adopts a distorted trigonal-bipyramidal geometry with one equatorial coordination site filled by a stereochemically active lone pair, forming a linear (Tl· · · Au· · · )∞ chain, as shown in Fig. 19.6.11(b). In contrast, the pentachlorophenyl complex comprises an infinite zigzag (Tl· · · Au· · · Tl% · · · Au· · · )∞ chain constructed from two kinds of thallium(I) centers with distorted trigonal-pyramidal and pseudo-tetrahedral geometries for Tl and Tl% (each possessing a stereochemically active lone pair), respectively, as shown in Fig. 19.6.12. C6F5 Tl N

N

C6F5

N Tl N

Au

C6F5

C6F5 Au

C6F5

Tl 340.92 pm

N

C6F5

Tl

N

N

Tl N

C6F5

Au

Au

C6F5

C6F5

N

N N

N

C6F5

C6F5

Tl

Tl

Tl

N

C6F5

Au

N

N

N

Au

C6F5

N

Au

C6F5

N

C6F5 Au

N

C6F5

C6F5

N

N

N

Au

C6F5

N

Tl

Au

C6F5

Tl

Tl

Tl

Tl

Au

N

N

C6F5

Au

N

Tl

C6F5

C6F5

C6F5

N

301.61

N

C6F5

N

C6F5

C6F5

Au

Au

C6F5

C6F5

N Tl N N

Tl

Fig. 19.6.13.

Layer structure of [AuTl(C6 F5 )2 (bipy)]n . The bridging 4,4’-bypyridine ligand is represented by a thick rod joining its two terminal N atoms.

Metal–Metal Bonds N

N

N C6Cl5

Tl'

Au

Tl

Tl

C6Cl5

Tl'

Au

THF

C6Cl5

N

C6Cl5

N N Tl'

THF

Tl'

C6Cl5

Au C6Cl5

C6Cl5

N

Au

Tl

C6Cl5

N

C 6 Cl5

N

N

N Tl

C 6 Cl5 N

C6Cl5

N

C6Cl5

N Tl' THF

C6Cl5

C6Cl5

Tl

C 6 Cl5

C 6 Cl5

N N

C6Cl5

Tl'

Au

THF

C6Cl5

N Au

Au

Au

Tl

C6Cl5

N

C6Cl5

N

C 6 Cl5

N

Au

Au

Tl

N

C 6 Cl5

C6Cl5

N

Au

THF

C6Cl5

N

THF

C 6 Cl5

N

Tl'

Au

Tl

Tl'

Au

C6Cl5

N

N

C 6 Cl5

Au THF

C 6 Cl5

N N

C6Cl5

N

N

Au

C6Cl5

N

C 6 Cl5

Au

THF N

N

N

N

731

N Tl'

THF

C6Cl5

N

C6Cl5

C6Cl5

N

Au

Au Tl

C6Cl5

C6Cl5

N

N

N

N

Tl'

Tl'

Tl'

Fig. 19.6.14.

Layer structure of [Au2 Tl2 (C6 Cl5 )4 (bipy)1.5 (THF)]n . Atom Tl is shown in boldface type to distinguish it from atom Tl% . Each bridging 4,4’-bypyridine ligand is represented by a thick rod joining the terminal N atoms.

Similar acid–base reactions with the introduction of the exo-bidentate bridging ligand 4,4, -bipyridine led to the formation of [AuTl(C6 F5 )2 (bipy)]n and [Au2 Tl2 (C6 Cl5 )4 (bipy)1.5 (THF)]n , which exhibit higher-dimensional polymeric structures. In the pentafluorophenyl complex, linear tetranuclear Tl· · · Au· · · Au· · · Tl units are linked through bipyridine bridges to form a honeycomb-like network, as shown in Fig. 19.6.13. The pentachlorophenyl complex contains two kinds of thallium(I) centers: atom Tl is coordinated by two bipyridyl N atoms, whereas atom Tl% is bound to a THF ligand and a bipyridyl N atom, as shown in Fig. 19.6.14. The asymmetric unit contains two non-equivalent bridging 4,4, -bipyridine ligands, one of which occupies a 1¯ site in the unit cell and necessarily exists in the planar configuration. Hetero-metallophilic interaction generates infinite (Tl· · · Au· · · Tl% · · · Au· · · )∞ zigzag chains linked by the first kind of bridging bipyridine ligand (located in a general position and nonplanar) across Tl and Tl% to form a brick-like layer. The centrosymmetric bipyridine, which is bound to Tl and represented by a dangling rod in the figure, connects the Tl atoms in adjacent layers to form a double layer.

References 1. F. A. Cotton, G. Wilkinson, C. A. Murillo and M. Bochmann, Advanced Inorganic Chemistry, 6th edn., Wiley, New York, 1999.

732

Structural Chemistry of Selected Elements 2. F. A. Cotton, C. A. Murillo and R. A. Walton (eds.), Multiple Bonds between Metal Atoms, 3rd edn., Springer, New York, 2005. 3. F. P. Purchnik, Organometallic Chemistry of the Transition Elements, Plenum Press, New York, 1990. 4. D. M. P. Mingos and D. J. Wales, Introduction to Cluster Chemistry, Prentice Hall, Englewood Clifts, NJ, 1990. 5. D. F. Shriver, H. D. Karsz and R. D. Adams (eds.), The Chemistry of Metal Cluster Complexes, VCH, New York, 1990. 6. P. J. Dyson and J. S. McIndoe, Transition Metal Carbonyl Cluster Chemistry, Gordon and Breach, Amsterdam, 2000. 7. M. H. Chisholm (ed.), Early Transition Metal Clusters with π -Donor Ligands, VCH, New York, 1995. 8. M. Gielen, R. Willem and B. Wrackmeyer (eds.), Unusual Structures and Physical Properties in Organometallic Chemistry, Wiley, West Sussex, 2002. 9. T. P. Fehlner (ed.), Inorganometallic Chemistry, Plenum Press, New York, 1992. 10. J.-X. Lu (ed.), Some New Aspects of Transition-Metal Cluster Chemistry, Science Press, Beijing/New York, 2000. 11. P. Braunstein, L. A. Oro and P. R. Raithby (eds.), Metal Clusters in Chemistry: vol. 1 Molecular Metal Cluster; vol. 2 Catalysis and Dynamics and Physical Properties of Metal Clusters; vol. 3 Nanomaterials and Solid-state Cluster Chemistry, Wiley– VCH, Weinheim, 1999. 12. A. J. Welch and S. K. Chapman (eds.), The Chemistry of the Copper and Zinc Triads, Royal Society of Chemistry, Cambridge, 1993. 13. J. P. Collman, R. Boulatov and G. B. Jameson, The first quadruple bond between elements of different groups. Angew. Chem. Int. Ed. 40, 1271–4 (2001). 14. T. Nguyen, A. D. Sutton, M. Brynda, J. C. Fettinger, G. J. Long and P. P. Power, Synthesis of a stable compound with fivefold bonding between two chromium(I) centers.Science 310, 844–7 (2005). 15. G.-D. Zhou, Bond valence and molecular geometry. University Chemistry (in Chinese) 11, 9–18 (1996). 16. P. Pyykkö, Strong closed-shell interaction in inorganic chemistry. Chem. Rev. 97, 579–636 (1997). 17. N. Kaltsoyannis, Relativistic effects in inorganic and organometallic chemistry. J. Chem. Soc. Dalton Trans., 1–11 (1997). 18. S.-M. Peng, C.-C. Wang, Y.-L. Jang, Y.-H. Chen, F.-Y. Li, C.-Y. Mou and M.-K. Leung, One-dimensional metal string complexes. J. Magn. Magn. Mater. 209, 80–3 (2000). 19. C.-H. Chien, J.-C. Chang, C.-Y. Yeh, G.-H. Lee, J.-M. Fang, Y. Song and S.-M. Peng, Dalton Trans., 3249–56 (2006). 20. J. K. Bera and K. R. Dunbar, Chain compounds based on transition metal backbones: new life for an old topic. Angew. Chem. Int. Ed. 41, 4453–7 (2002). 21. E. J. Fernández, A. Laguna, J. M. López-de-Luzuriaga, F. Mendizábal, M. Monge, M. E. Olmos and J. Pérez, Theoretical and photoluminescence studies on the d10 − s2 AuI −TlI interaction in extended unsupported chains. Chem. Eur. J. 9, 456–65 (2003).

Supramolecular Structural Chemistry

20.1

Introduction

Supramolecular chemistry is a highly interdisciplinary field of science covering the chemical, physical, and biological features of molecular assemblies that are organized and held together by intermolecular interactions. The basic concepts and terminology were introduced by J.-M. Lehn, who together with D. J. Cram and C. J. Pedersen were awarded the 1987 Nobel Prize in Chemistry. In the words of Lehn, supramolecular chemistry may be defined as chemistry beyond the molecule, i.e., the study of organized entities of higher complexity (supermolecule) resulting from the association of two or more chemical species consolidated by intermolecular forces. The relationship of supermolecules to molecules and intermolecular binding is analogous to that of molecules to atoms and covalent bonds (Fig. 20.1.1). A clarification about vocabulary in the chemical literature: the prefix in the word supermolecule (a noun) is derived from the Latin super, meaning “more than” or “above”; it should not be used interchangeably with the prefix supra in the word supramolecular (an adjective), which means “beyond” or “at a higher level than.” 20.1.1

Intermolecular interactions

Intermolecular interactions constitute the core of supramolecular chemistry. The design of supermolecules requires a clear understanding of the nature, strength, and spatial attributes of intermolecular bonding, which is a generic term that includes ion pairing (Coulombic), hydrophobic and hydrophilic interactions, hydrogen bonding, host–guest complementarity, π –π stacking, and van der Waals interactions. For inorganic systems, coordination bonding is included in this list if the metal acts as an attachment template. Intermolecular interactions in organic compounds can be classified as (a) isotropic, medium-range forces that define molecular shape, size, and close packing and (b) anisotropic, longrange forces, which are electrostatic and involve heteroatom interactions. In general, isotropic forces (van der Waals interactions) usually mean dispersive and repulsive forces, including C · · · C, C · · · H, and H · · · H interactions, while most interactions involving heteroatoms (N, O, Cl, Br, I, P, S, Se, etc.) with one another or with carbon and hydrogen are anisotropic in character, including ionic forces, strongly directional hydrogen bonds (O–H · · · O, N–H · · · O),

20

734

Structural Chemistry of Selected Elements MOLECULAR

SYNTHESIS A, B, C, D,... covalent bonds

SUPRAMOLECULAR

POLYMOLECULAR organized assemblies

RECEPTOR recognition COMPLEXATION intermolecular interaction

SUPERMOLECULE

MOLECULAR and SUPRAMOLECULAR DEVICES

transformation translocation

SUBSTRATE

functional components

Fig. 20.1.1.

Conceptual development from molecular to supramolecular chemistry: molecules, supermolecules, molecular devices, and supramolecular devices.

weakly directional hydrogen bonds (C–H · · · O, C–H · · · N, C–H · · · X, where X is a halogen, and O–H · · · π), and other weak forces such as halogen · · · halogen, nitrogen · · · nitrogen, and sulfur · · · halogen interactions. In a crystal, various strong and weak intermolecular interactions coexist (sometimes in delicate balance, as is demonstrated by the phenomenon of polymorphism) and consolidate the three-dimensional scaffolding of the molecules. (b) O

O NH

(a) H3C

Fig. 20.1.2.

Molecular recognition through hydrogen bonding of (a) adenine in a cleft, and (b) barbituric acid in a macrocyclic receptor (right).

H3C H3C

20.1.2

H

N O O N R N H O N N H O NH N N O H N H O

N

CH3 O

CH3

NH O

H O

N

O

H N

N H O

N H

O

N

O

CH3

Molecular recognition

The concept of molecular recognition has its origin in effective and selective biological functions, such as substrate binding to a receptor protein, enzyme reactions, assembly of protein–DNA complexes, immunological antigen–antibody association, reading of the genetic code, signal induction by neurotransmitters, and cellular recognition. Many of these functions can be performed by artificial receptors, whose design requires an optimal match of the steric and electronic features of the non-covalent intermolecular forces between substrate and receptor. Some of the recognition processes that have been well studied by chemists include spherical recognition of metal cations by cryptates, tetrahedral recognition by macrotricyclic cryptands, recognition of specific anions, and the binding and recognition of neutral molecules through Coulombic, donor–acceptor, and in particular hydrogen-bonding interactions (see Fig. 20.1.2).

Supramolecular Structural Chemistry O 1

O

O O

H O

735

π−π Stacking

2

O

+

+

+

+

+

+

+

+

O O 2 H O

+

+

N+

N

+

+

+ [1.2]4+

+

N+

N

Fig. 20.1.3.

24+ Primary Structure

Supermolecule

Supermolecule array

Macroscopic conglomerate

Molecular recognition studies are typically carried out in solution, and the effects of intermolecular interactions are often probed by spectroscopic methods. 20.1.3

Self-assembly

The term “self-assembly” is used to designate the evolution toward spatial confinement through spontaneous connection of molecular components, resulting in the formation of discrete or extended entities at either the molecular or the supramolecular level. Molecular self-assembly yields covalent structures, while in supramolecular self-assembly several molecules spontaneously associate into a single, highly structured supramolecular aggregate. In practice, self-assembly can be achieved if the molecular components are loaded with recognition features that are mutually complementary; i.e., they contain two or more interaction sites for establishing multiple connections. Thus well-defined molecular and supramolecular architectures can be spontaneously generated from specifically “engineered” building blocks. For example, self-assembly occurs with interlocking of molecular components using π–π interactions (Fig. 20.1.3) and the formation of capsules with some curved molecules bearing complementary hydrogen bonding sites (Fig. 20.1.4). The cyclic octapeptide cyclo-[–(D-Ala–L-Glu–D-Ala–L-Gln)2 –] has been designed by Ghadiri and co-workers to generate a hydrogen-bonded organic nanotube having an internal diameter of approximately 0.7–0.8 nm (Fig. 20.1.5). 20.1.4

Crystal engineering

Structural chemists and crystallographers rightfully regard an organic crystal as the “supermolecule par excellence,” being composed of Avogadro’s number of molecules self-assembled by mutual recognition at an amazing level of precision. In contrast to a molecule, which is constructed by connecting atoms with covalent bonds, a molecular crystal (solid-state supermolecule) is built by connecting molecules with intermolecular interactions. The process of

Aspects of supramolecular hierarchy in increasing superstructural complexity.

736

Structural Chemistry of Selected Elements

I

O

O

H N

N

Ph

Ph N

H

N H

N Ph

N

N

N

O

H

H

O

O

O

O

O

H

self-assembly

O

III

H N

H

N Ar

N

H N

N

Ar

N

N

O

H

O N

R

SO 2

H

H

R N

N

H O

O

O

N

N

N

N O

O H

O

O

O

H

H O

O

II

H

H

Ph

N

N H

N

N

R

R

H

O

Fig. 20.1.4.

A tennis-ball-shaped molecular aggregate can be constructed by the self-assembly of curved molecule I. Tetrameric assembly of II generates a pseudo-spherical capsule. Dimeric assembly of III can be induced by the encapsulation of smaller molecules of appropriate size and shape at the center of a spherical complex.

NH2

(a)

HN

O O

C

O C

CH3

H N

D

L

OH C

O

L

O NH C O

HN D

H3C O C HN O OH

D L

C N O H

L

D C CH O

(c)

CH3 NH C O

NH

3

O NH2

0.7–0.8 nm (b) H ON C C O N H

O C N H H N C O

H O N C N C O O HH N C N C H O

Fig. 20.1.5.

(a) Structural formula of cyclo-[–(d-Ala–l-Glu–d-Ala–l-Gln)2 –]; Ala = alanine, Glu = glutamic acid, Gln = glutamine, d or l indicates chirality at the carbon atom. (b) Perspective view of the backbone of the flat, ring-shaped octapeptide. (c) Tubular architecture generated from a stack of octapeptide molecules held by intermolecular hydrogen bonding.

Supramolecular Structural Chemistry

737

Table 20.1.1. Comparison of crystal engineering and molecular recognition

(1) (2) (3)

(4)

(5) (6)

(7)

(8)

Crystal engineering

Molecular recognition

Concerned with the solid state Considers both convergent and divergent binding of molecules Intermolecular interaction are examined directly in terms of their geometrical features obtained from X-ray crystallography Design strategies involve the control of the threedimensional arrangement of molecules in the crystal; such an arrangement ideally results in desired chemical and physical properties Both strong and weak interactions are considered independently or jointly in the design strategy The design may involve either single-component species or multicomponent species; a single-component molecular crystal is a prime example of self-recognition In host–guest complexes, the host cavity is composed of several molecules whose synthesis may be fairly simple; the geometry and functionality of the guest molecules are often of significance in the complexation Systematic retrosynthetic pathways may be deduced with the Cambridge Structural Database (CSD) to design new recognition patterns using both strong and weak interactions

Concerned mainly with solution phase Most cases only focus on convergent binding of molecules Intermolecular interactions are studied indirectly in terms of association constants obtained from various spectroscopic (NMR, UV, etc.) methods Design strategies are confined to the mutual recognition of generally two species: the substrate and the receptor; such recognition is expected to mimic some biological functionality Only strong interactions such as hydrogen bonding are generally used for the recognition event The design usually involves two distinct species: the substrate and the receptor; ideas concerning self-recognition are poorly developed In host–guest complexes, the host cavity is often a single macrocyclic molecule whose synthesis is generally tedious; the host framework rather than the guest molecule plays a critical role in the complexation There is no systematic set of protocols for the identification of new recognition patterns; much depends on individual style and preferences

crystallization is one of the most precise and spectacular examples of molecular recognition. The determination of crystal structures by X-ray crystallography provides precise and unambiguous data on intermolecular interactions. Crystal engineering has been defined by Desiraju as “the understanding of intermolecular interactions in the context of crystal packing and in the utilization of such knowledge in the design of new solids with desired physical and chemical properties.” Crystal engineering and molecular recognition are twin tenets of supramolecular chemistry that depend on multiple matching of functionalities among molecular components. Historically, crystal engineering has been developed by structural and physical chemists with a view to design new materials and solid-state reactions, whereas molecular recognition has been developed by physical organic chemists interested in mimicking biological processes. The methodologies and goals of these two related fields are summarized in Table 20.1.1. 20.1.5

Supramolecular synthon

In the context of organic synthesis, the term “synthon” was introduced by Corey in 1967 to refer to “structural units within molecules which can be formed and/or assembled by known or conceivable synthetic operations.” This general definition was modified by Desiraju for supramolecular chemistry: “Supramolecular synthons are structural units within supermolcules which can be formed and/or

738

Structural Chemistry of Selected Elements assembled by known or conceivable synthetic operations involving intermolecular interactions.” The goal of crystal engineering is to recognize and design synthons sufficiently robust to be carried over from one network structure to another, which ensures generality and predictability. Some common examples of supramolecular synthons are shown in Fig. 20.1.6. It should be emphasized that supramolecular synthons are derived from designed combinations of interactions and are not identical to the interactions. A supramolecular synthon incorporates both chemical and geometrical recognition features of two or more molecular fragments, i.e., both explicit and implicit involvement of intermolecular interactions. However, in the simplest cases, a single interaction may be regarded as a synthon, for instance Cl · · · Cl, I · · · I or N · · · Br [Figs. 20.1.6(23–25)]. Besides the strong hydrogen bonds (N–H · · · O and O–H · · · O), which are expected to be frequently involved in supramolecular synthons [Figs. 20.1.6(1–5)], weak hydrogen bonds of the C–H···X variety and π–π interactions may also be significant. Although such weaker interactions have low energies in the range of 2 to 20 kJ mol−1 , their cumulative effects on molecular association and crystal structure and packing are just about as predictable as the effects of conventional hydrogen bonding. The nature of the X · · · X interaction in trimer synthon 44 is illustrated in Fig. 20.1.7. The C–X bond in a halo-substituted phenyl ring is polarized, so that there are regions of positive and negative electrostatic potentials around the X atom. The cyclic interaction of three C–X groups optimizes electrostatic potential overlap in the halogen trimer system.

20.2

Hydrogen-bond directed assembly

Hydrogen bonding is an indispensable tool for designing molecular aggregates within the fields of supramolecular chemistry, molecular recognition, and crystal engineering. It is well recognized that in organic crystals certain building blocks or supramolecular synthons have a clear pattern preference, and molecules that contain these building blocks tend to crystallize in specific arrangements with efficient close packing. As already mentioned in Section 11.2.1, three important rules are generally applicable to the formation of hydrogen bonds between functional groups in neutral organic molecules: (a) all strong donor and acceptor sites are fully utilized; (b) intramolecular hydrogen bonds giving rise to a six-membered ring will form in preference to intermolecular hydrogen bonds; and (c) the remaining proton donors and acceptors not used in (b) will form intermolecular hydrogen bonds to one another. For additional rules and a full discussion the reader is referred to the papers of Etter [Acc. Chem. Res. 23, 120–6 (1990); J. Phys. Chem. 95, 4601–10 (1991)]. Figure 20.2.1 shows a hydrogen-bonded polar sheet where 3,5-dinitrobenzoic acid and 4-aminobenzoic acid are co-crystallized.

Supramolecular Structural Chemistry O

2

1

O

H O

O H

O

3

4

O O H

O

H

N N 10

H

7

O

N N

N H

O

O

H

O H

11

H

8

H

H

H

O N O

N O

O N O

5

H N

N N

O

C N

O N O

N H

H N

N

O H N

H N

H N

Cl

Cl

I

I

H O

H O H

N N

31

H

C C

N

O

Cl

N C

O H 21

N

N

N

H N

H N

H N

N

N

N

22

N H

N

H

O

O

O

O

H

H

O H

H O

H

Br 29

28

N

Cl

N

N

H N

Cl

C

H

C

(continued on next page)

Cl

O

O

N H

H

Fig. 20.1.6.

C N

H

O

32

N

O

25

27

26

N

H

N C

N H

N

H N

H

N H

I

24

23

H

20

O

H

17

19

O

O N O

13

16

O N O

18

O

Cl

Cl

H N

H

12

O

15

14

9

O

O

H

O N O

H

H N

H O

6

O

739

N

N

C

Cl

Cl

C N

H N

N 33

Cl

N

30

H

C 34

C N

H

H

O

C

C H

O

N

C O

C

H C N

35

H2 C H2 C

CH2 CH2

CH2

H2 C H2 C

CH2 CH2 CH2

740

Structural Chemistry of Selected Elements 37

36

38

O

H

O

O H

N

O H

H N

O

O

H N

N

H N

O

H N

Br

Br

N

H

C H

Br

C

Br

C

O

47

C

Br Br

H O C

H

Br

N

C O

46

45

44

N H

H H

H C

N

43

H O

HN

O

42

N

N H

H N

O H O

N

41

40

39

C

C

N

C

C

H O

H

H

O

H

O

H

O H O

48

O C C H

N O

Fig. 20.1.6. (continued)

Representative supramolecular synthons. Synthon Nos. 1–35 are taken from G. R. Desiraju, Angew. Chem. Int. Ed. 34, 2311 (1995). Nos. 33: known as EF (edge-to-face). and 34, OFF (offset face-to-face) phenyl-phenyl interactions from, M. L. Scudder and I. G. Dance, Chem. Eur. J. 8, 5456 (2002); I. Dance, Supramolecular inorganic chemistry, in G. R. Desiraju (ed.), The Crystal as a Supramolecular Entity, Perspectives in Supramolecular Chemistry, vol. 2, Wiley, New York, 1996, pp. 137–233; 36 from T. Steiner, Angew. Chem. Int. Ed. 41, 48 (2002); 37 from A. Nangia, CrystEngComm 17, 1 (2002); 38 from P. Vishweshwar, A. Nangia and V. M. Lynch, CrystEngComm 5, 164 (2003); 39 from F. H. Allen, W. D. S. Motherwell, P. R. Raithby, G. P. Shields and R. Taylor, New J. Chem., 25 (1999); 40 from R. K. Castellano, V. Gramlich and F. Diederich, Chem. Eur. J. 8, 118 (2002); 41 from C.-K. Lam and T. C. W. Mak, Angew. Chem. Int. Ed. 40, 3453 (2001); 42 from M. D. Hollingsworth, M. L. Peterson, K. L. Pate, B. D. Dinkelmeyer and M. E. Brown, J. Am. Chem. Soc. 124, 2094 (2002); 43, observed in classical hydroquinone clathrates and phenolic compounds, from T. C. W. Mak and B. R. F. Bracke, Hydroquinone clathrates and diamondoid host lattices, in D. D. MacNicol, F. Toda and R. Bishop (eds.), Comprehensive Supramolecular Chemistry, vol. 6, Pergamon Press, New York, 1996, pp. 23–60; 44 from C. K. Broder, J. A. K. Howard, D. A. Keen, C. C. Wilson, F. H. Allen, R. K. R. Jetti, A. Nangia and G. R. Desiraju, Acta Crystallogr. B56, 1080 (2000); 45 from D. S. Reddy, D. C. Craig and G. R. Desiraju, J. Am. Chem. Soc. 118, 4090 (1996); 46 from B. Goldfuss, P. v. R. Schleyer and F. Hampel, J. Am. Chem. Soc. 119, 1072 (1997); 47 from P. J. Langley, J. Hulliger, R. Thaimattam and G. R. Desiraju, New J. Chem., 307 (1998); 48 from B. Moulton and M. J. Zaworotko, Chem. Rev. 101, 1629 (2001).

20.2.1

Supramolecular architectures based on the carboxylic acid dimer synthon

Carboxylic acids are commonly used as pattern-controlling functional groups for the purpose of crystal engineering. The most prevalent hydrogen bonding patterns formed by carboxylic acids are the dimer and the catemer. Carboxylic acids containing small substituent groups (formic acid, acetic acid) form the catemer motif, while most others (especially aromatic carboxylic acids) form

Supramolecular Structural Chemistry

741

negative electrostatic potenial

(a)

X

positive electrostatic potenial

C

(b) Fig. 20.1.7.

(a) Areas of positive and negative electrostatic potentials at the halogen substituent of a phenyl ring and (b) stabilization of the X · · · X trimer supramolecular synthon 44.

dimers, although not exclusively. In the case of di- and polycarboxylic acids, terephthalic acid, and isophthalic acid form linear and zigzag ribbons (or tapes), respectively, trimesic acid (1,3,5-benzenetricarboxylic acid) with its threefold molecular symmetry forms a hydrogen-bonded sheet, and adamantane-1,3,5, 7-tetracarboxylic acid forms a diamondoid network (Fig. 20.2.2). H O

O

O

O N

O N

N

H

O

O

O

O H

N

O

O

O N

O H NO

O H

O

N

H

H O

O

O N

O H

H O

O

H

H O

H NH O O N NO O

O N

O H

H O

O

H

H

O

O

H

N

H

O

O

O

O H

H O

O

O O H NH NO O N

O ON

O H

O

O N

O N

O N

O H

O

O H O

H NH O

O

If a bulky hydrophobic group is introduced at the 5-position of isophthalic acid, a cyclic hexamer (rosette) is generated. In the crystal structure of trimesic acid, the voids are filled through interpenetration of two honeycomb

Fig. 20.2.1.

Polar sheet formed by 3,5-dinitrobenzoic acid and 4-aminobenzoic acid using the nitro-amine and carboxylic acid dimer motif.

742

Structural Chemistry of Selected Elements H O

(a)

O

O

O H

O

O

(b)

H

HO O

O H

H

O

O

O H O

(c)

H

H

O H

O

H

O

O

O

O

H O

O

O

O

H

H

O

O

O

O O

H O

O H

O

O

H O

O H

O H O

O H O

H

O

O

O

O O H

O H

O

O

HO

O

O H

H O

H

H O

O

O H

O

(d)

O

O

O

O H

(a) One-dimensional linear tape and (b) crinkled (or zigzag) tape, (c) two-dimensional sheet (or layer), and (d) three-dimensional network (or framework) held together by the carboxylic acid dimer synthon.

O

O

H

H

H

O

O

1.4 nm

O

H

H O O

O

Fig. 20.2.2.

O

O

O H

O O

O

HO

O

O

O H

O

O

O

H

O

O

H

O

H O

O

H O

O H

H

O

O

O

H O O

H O

networks with additional stabilization by π–π stacking interactions. In the host lattice of adamantane-1,3,5,7-tetracarboxylic acid, the large voids are filled by interpenetration and small guest molecules. 20.2.2

Graph-set encoding of hydrogen-bonding pattern

The robust intermolecular motifs found in organic systems can be used to direct the synthesis of supramolecular complexes in crystal engineering. In the interest

Supramolecular Structural Chemistry

743 O

O O

Ph H

O

R Ph

P

N

Ph

O

H

O

H

R

D

C(4)

O

O H

H

N

S(6)

H O

O O

H O

N H

H

R22 (8)

N

O

H

R22 (8)

Some examples of graph-set descriptors of hydrogen-bonded structural motifs.

of adopting a systematic notation for the topology of hydrogen-bonded motifs and networks, a graph-set approach has been suggested by Etter and Ward. This provides a description of hydrogen-bonding schemes in terms of four pattern designators (G), i.e., infinite chain (C), ring (R), discrete complex (D), and intramolecular (self-associating) ring (S), which together with the degree of the pattern (n, the number of atoms comprising the pattern), the number of donors (d ), and the number of acceptors (a) are combined to form the quantitative graph-set descriptor Gda (n). Examples of the use of these quantitative descriptors are given in Fig. 20.2.3. Preferable hydrogen-bonding patterns of a series of related compounds containing a particular type of functional group can be obtained by graph-set analysis. For example, most primary amides prefer forming cyclic dimers and chains with a common hydrogen-bonding pattern C(4)[R12 (6)]. Furthermore, important insights may be gained by graph-set analysis of two seemingly unrelated organic crystals, which may lead to similar hydrogen-bonding patterns involving different functional groups. Some of the most common supramolecular synthons found in the Cambridge Structure Database are illustrated below:

O

O H O

R22(8)

N H N

N H N

R22(8)

N H O

O H N

R22(8)

O N H H

C(4)[R21 (6)]

Fig. 20.2.3.

O H

N H H

H N H

H

O H

O

R22(4)

The same set of hydrogen bond donors and acceptors may be connected in alternate ways to generate distinguishable motifs, giving rise to different

H N H O

N H H

744

Structural Chemistry of Selected Elements (a) O HN O

O N

Et Et

H H

Et Et N

O

N

(c) O

O HN O

(b) O H O

N

O N

Et Et

H

O

Fig. 20.2.4.

Patterns of hydrogen bonding found in three polymorphic forms of 5,5-diethylbarbituric acid. The graph-set descriptors are (a) C(6)[R22 (8)R24 (12)], (b) C(10)[R22 (8)], and (c) C(6)[R22 (8)R44 (16)].

O

H

H H O

Et Et N

N

O

N

Et Et

H

Et Et N

N

H O

O

H

O

O HN O

H

O

N

Et Et

H

Et Et N

N

O H

O

O

O

polymorphic forms. A good example is 5,5-diethylbarbituric acid, for which three crystalline polymorphs that exhibit polymeric ribbon structures are shown in Fig. 20.2.4.

20.2.3

Supramolecular construction based on complementary hydrogen bonding between heterocycles

The simple heterocyclic compounds melamine and cyanuric acid possess perfectly matched sets of donor/acceptor sites, 6/3 and 3/6 respectively, for complementary hydrogen bonding to form a planar hexagonal network (Fig. 20.2.5). Three distinct structural motifs can be recognized in this extended array: (a) linear tape,, (b) crinkled tape and (c) cyclic hexameric aggregate (rosette). Using barbituric acid derivatives and 2,4,6-triaminopyrimidine derivatives, the group of Whitesides has successfully synthesized all three preconceived systems. The conceptual design involves disruption of N–H · · · O and N–H · · · N hydrogen bonding in specific directions by introducing suitable hydrophobic bulky groups (Fig. 20.2.6). The group of Reinhoudt has reported the construction of a D3 hydrogenbonded assembly of three calix[4]arene bismelamine and six barbituric acid derivatives (Fig. 20.2.7).

20.2.4

Hydrogen-bonded networks exhibiting the supramolecular rosette pattern

Ward has shown that the self-assembly of cations and anions in a guanidinium sulfonate salt, through precise matching of donor and acceptor sites, gives rise to a layer structure displaying the rosette motif, which is not planar but corrugated since the configuration at the S atom is tetrahedral (Fig. 20.2.8). If the sulfonate R group is small, a bilayer structure with interdigitated substituents is formed [structural motif (a)]. When R is large, a single layer structure with substituents alternating on opposite sides of the hydrogen-bonded layer is obtained [motif (b)]. Alternatively, the use of disulfonates provides covalent linkage between

Supramolecular Structural Chemistry H

H

N

O N

H

H

cyanuric acid

N H

H

N H

N

N

H N

N

N O

H

O

H

N N

H

N

H

H

H N H

N

H

H

H N N

H H

O N H

H

O

H

H N

N N H

H

H

H

H H N H

H N N

N

N H

N

N

H

N

H

N

N H

H H

N

H H

N H

N

H

O N

H

H

(a)

O N

H H

O H

N H

O N H

H N N

N

H N

N N

N H

N

N

H

H

N

H

N

N H O

O

H

H

(c) H

N

N H

N H

H H

O

H

O

O

O H

N

O N

N

H

O

N

O

H

H N

N

N

N H

H

N

N

N

N H

N

O

N H

O H

N N

H

N

O

H

O

O N H

N

O N

N

N

N

H

N

O H

H N

H

N H

H

N

N H

H

N

N

N

O

N

N H

H N

N H

melamine

H

N

N

O

N

H

N

H

H

H

O

O

H

N H

H N

N N

H

N

O

N

O

N

H

O

H

H

H

N

O

745

H

N

N N H

H N

N

N H

(b)

Fig. 20.2.5.

Hexagonal layer structure of the 1:1 complex of melamine and cyanuric acid. Three kinds of assembly in lower dimensions are possible: (a) linear tape, (b) crinkled tape, and (c) rosette.

adjacent layers to generate a pillared three-dimensional network, which may enclose a variety of guest species G [motif (c)]. The design and construction of hydrogen-bonded “supramolecular rosettes” from guanidinium/organic sulfonate, trimesic acid, or cyanuric acid/melamine depend on utilization of their topological equivalence, i.e., equal numbers of donor and acceptor hydrogen bonding sites and C3 symmetry of the component moieties. As a modification of this strategy, a new kind of “fused-rosette ribbon” can be constructed with the guanidinium cation (GM+ ) and hydrogen carbonate dimer (HC− )2 in the ratio of 1:1 (Fig. 20.2.9). Each supramolecular rosette comprises a quasi-hexagonal assembly of two GM+ and four HC− units connected by strong NGM –H · · · OHC and OHC –H · · · OHC hydrogen bonds. The (HC− )2 dimer is shared as a common edge of adjacent rosettes and makes full use of its remaining acceptor sites in linking with GM+ . On the other hand, each GM+ in the resulting linear ribbon (or tape) still possesses a pair of free donor sites, and it is anticipated that some “molecular linker” with suitable acceptor sites may be used to bridge an array of parallel ribbons to form a sheet-like network. This design objective has been realized in the synthesis and characterization of the inclusion compound − + − 5[C(NH2 )+ 3 ]·4(HCO3 )·3[(n-Bu)4 N ]·2[1,4-C6 H4 -(COO )2 ]·2H2 O with the 2− terephthalate (TPA ) anion functioning as a linker.

H

746

Structural Chemistry of Selected Elements R

R

R

O H

N

H

H H

R

R

O H

N O

N

N

H

O

N

N

N R'

H

N

H

H

H

H N

R'

N

H

H N

H

H

N

N H

N

N R'

H

H

N

H

N N

N

H

H

H

N

N

H

N

N

H N

O H

N

N H

R = Et, R' = Bu O R

N

R O

N R'

N

H

H

H

H

O

O H

R

N

H

N

R

H R'

N

H O

N

H

O N

H

H

O N

N O

H

R

H H

R' N

N

R'

N

O

H

(a)

(b)

H

N O

H

N

H

R

N

N

N

H

N

R

O H

H

O H

N

N

H

R O

H

H

O N

H

H

N

R

O

O

H

H

Fig. 20.2.6.

(a) Linear tape and (b) rosette 1:1 complexes constructed with barbituric acid derivatives and 2,4,6-triaminopyrimidine derivatives.

As shown in Fig. 20.2.10, each HC− provides one donor and one acceptor site to form a planar dimer motif [A, R22 (8)]. The remaining eight acceptor sites of each (HC− )2 dimer are topologically complemented by four GM+ units, such that each GM+ connects two (HC− )2 dimers through two pairs of N–Hsyn · · · O hydrogen bonds [B, R22 (8)]. Thus two GM+ units and two (HC− )2 dimers constitute a planar, pseudo-centrosymmetric, quasi-hexagonal supramolecular rosette [C, R46 (12)] with inner and outer diameters of approximately 0.55 and 0.95 nm, respectively. In the resulting fused-rosette ribbon, the remaining two exo-orientated donor sites of each GM+ unit form a pair of N– Hanti · · · O hydrogen bonds [D, R22 (8)] with a TPA2− carboxylate group. Thus two types of ladders are developed: type (I) [TPA2− composed of C(10) to C(17) and O(13) to O(16)] is consolidated by two independent water molecules that alternately bridge carboxylate oxygen atoms of neighboring steps by pairs of donor Ow –H· · · O hydrogen bonds, generating a centrosymmetric ring motif [E, R44 (22)] and pentagon pattern [F, R36 (12)]; in the type (II) ladder [TPA2− composed of C(18) to C(25) and O(17) to O(20)], carboxylate oxygen atoms O(18),

H

Supramolecular Structural Chemistry NH2 N BuHN X

NH2

N

N NH

N

747

OPr

HN

N NHBu X

N

PrO

OPr

PrO

O H

O N

N

H

O

O NHBu N HN

H

N N

N

O N

N

H

O

H

H

Fig. 20.2.7.

D3 -symmetric hydrogen-bonded assembly of three calix[4]arene bismelamine and six barbituric acid derivatives.

O

R O S O

R O

S O– O

+ NH2

+ NH2 NH2

H H

(a)

(b)

N H

N

H

H

H N H

N H O

H

N

R O S O

H N H

R O S O

O

H

H H

N H

N

O H

H

H N H

N H O

H

N

H N H

R O S O

R O S O

H

H H

N H

N

H N H

H

(c) Fig. 20.2.8.

G

Top: assembly of guanidinium and sulfonate groups by N–H · · · O hydrogen bonds to give a corrugated rosette layer. Bottom: structural motifs (a), (b), and (c), which are formed depending on the size of R and the nature of the sulfonate group used.

748

Structural Chemistry of Selected Elements H H

N

N C

H

H O H

N

H

N

H

N

C

GM +

O

C

C O

H

O

H

N H H

N

N

O

O

O

H

O

C

rosette tape N

H

N

H

C

H H

H

H H

O

N O

O

H

H

H C

O

N C

O

H

N

O H

H

H

(HC-)2

C

O

C H

O

C

N

O

H

H

H H

O H

H

H O

O

N

O O

H

C

H

H

O

H C

O

Fig. 20.2.9.

Design of supramolecular rosette tape and linker. From T. C. W. Mak and F. Xue, J. Am. Chem. Soc. 122, 9860–1 (2000).

(II)

O

O

O

O

terephthalate dianion

(I)

08010 018 C19 C18 017

0

C8 07 012 01W C9 020N10 N2 09 011 014 016 C25 C11 C17 N11 C N3 C1 D C22 C4 C10 C14 019 N12 04 02 B N1 015 013 06 01 F 02W E A C7 C6 N5 N8 0503 C3 N7

N9

N4

C2 N6

Fig. 20.2.10.

Projection on (010) showing the two-dimensional network. Hydrogen bonds are represented by broken lines, and ring motifs A to F are shown in boldface type. The TPA2− ladders linking the rosette tapes are labeled (I) and (II).

Supramolecular Structural Chemistry

749

and O(19) belonging to adjacent steps are connected by the remaining GM+ ions, which are not involved in rosette formation, via two pairs of donor hydrogen bonds [G, R12 (6)] (Fig. 20.2.11(a)). The remaining two donor sites of each free GM+ ion are linked to a carboxylate oxygen atom and a water molecule of TPA2− column (I) of an adjacent layer to form a pentagon motif [H, R23 (8)], thus yielding a three-dimensional pillared layer structure (Fig. 20.2.11(b)). The large voids in the pillar region generate nanoscale channels extending along the [100] direction. The dimensions of the cross section of each channel are approximately 0.8 × 2.2 nm, within which three independent [(n-Bu)4 N]+ cations are aligned in separate columns in a well-ordered manner. (a)

(b)

O

H

O

O H H

H

H

N

G

G

N

O

H

N H

O

O

0.8 nm

H

2.2 nm

H

O

O

O

= TPA2–

= Rosette

= GM+

Fig. 20.2.11.

(a) Hydrogen-bonding motifs G and H involving linkage of the free guanidinium ion to neighboring rosette ribbon-terephthalate layers. (b) Schematic presentation of the pillared layer structure.

Drawing upon the above successful design of a linear “fused-rosette ribbon” assembled from the (HC− )2 dimer and GM+ in 1:1 molar ratio, it would be challenging to attempt the hydrogen-bond mediated construction of two premeditated anionic rosette-layer architectures using guanidinium and ubiquitous C3 -symmetric oxo-anions that carry unequal charges, namely guanidiniumcarbonate I and guanidinium-trimesate II, as illustrated in Fig. 20.2.12. In principle, the negatively charged, presumably planar network I can be combined with one molar equivalent of tetraalkylammonium ion R4 N+ of the right size as interlayer template to yield a crystalline inclusion compound 2− of stoichiometric formula (R4 N+ )[C(NH2 )+ 3 ]CO3 that is reminiscent of the graphite intercalates. Anionic network II, on the other hand, needs twice as many monovalent cations for charge balance, and furthermore possesses honeycomb-like host cavities of diameter ∼700 pm that must be filled by A A D

D

A D

D

A D

A

A D

A D

D

A D

A

Synthon D—A

A D

A D

Rosette Network

A D

D

A

N

H

O

I

[C(NH2 )3 +]

CO32–

N

H

O

II

[C(NH2 )3 +]

1,3,5-C6 H3 (COO– )3

C

Fig. 20.2.12.

Design of supramolecular rosette layers. From C.-K. Lam and T. C. W. Mak, J. Am. Chem. Soc. 127, 11536–7 (2005).

750

Structural Chemistry of Selected Elements suitable guest species. The expected formula of the corresponding inclusion − compound is (R4 N+ )2 [C(NH2 )+ 3 ] [1,3,5-C6 H3 (COO )3 ] · G, where G is an entrapped guest moiety with multiple hydrogen-bond donor sites to match the nearly planar set of six carboxylate oxygens that line the inner rim of each cavity. 2− Crystallization of (R4 N+ )[C(NH2 )+ 3 ]CO3 by variation of R, based on conceptual network I, was not successful. Taking into account the fact that the guanidinium ion can function as a pillar between layers and the carbonate ion is capable of forming up to twelve acceptor hydrogen bonds, as observed in crystalline bis(guanidinium) carbonate and [(C2 H5 )4 N+ ]2 ·CO2− 3 · 7(NH2 )2 CS [see Fig. 11.2.2(b)], the synthetic strategy was modified by incorporating a second guanidinium salt [C(NH2 )3 ]X as an extra component. After much experimentation with various combinations of R and X, the targeted construction of network I, albeit in undulating form, was realized through the isolation of crystalline 2− · 3(C O )2− · 2H O (1). 4[(C2 H5 )4 N+ ] · 8[C(NH2 )+ 2 4 2 3 ] · 3(CO3 ) In the asymmetric unit of (1), there are two independent carbonate anions and five independent guanidinium cations, which are henceforth conveniently referred to by their carbon atom labels in bold type. Carbonate C(1) and guanidinium C(3) each has one bond lying in a crystallographic mirror plane; together with carbonate C(2) and guanidinium C(4), they form a nonplanar zigzag ribbon running parallel to the b axis, neighboring units being connected by a pair of strong N+ –H· · · O− hydrogen bonds (Fig. 20.2.13). Adjacent anti-parallel {[C(NH2 )3 ]+ · CO2− 3 }∞ ribbons are further cross-linked by strong N+ –H· · · O− hydrogen bonds to generate a highly corrugated rosette layer, which is folded into a plane-wave pattern by guanidinium C(5) (Fig. 20.2.14). Guanidinium C(6) and C(7) protruding away from carbonate C(1) and C(2) are hydrogen-bonded to the twofold disordered oxalate ion containing C(8) and C(9) (Fig. 20.2.14), forming a pouch that cradles the disordered (C2 H5 )4 N+ ion. The carbonate ions C(1) and C(2) each form eleven acceptor hydrogen bonds, only one fewer than the maximum number. The resulting composite hydrogenbonded layers at x = 1/4 and 3/4 are interconnected by [(C2 O2− 4 · (H2 O)2 ]∞

c C1A

C4A

C2A C3A

Fig. 20.2.13.

Projection diagram showing a portion of the nonplanar anionic rosette network I concentrated at a = 1/4 in the crystal structure of (1). The atom types are differentiated by size and shading, and hydrogen bonds are indicated by dotted lines. Adjacent antiparallel {[C(NH2 )3 ]+ · CO2− 3 }∞ ribbons run parallel to the b axis. Symmetry transformations: A (1 /2 − x, 1 − y, 1 / + z); B (1 / − x, y − 1 / , z − 1 / ). 2 2 2 2

C2 C3

C4

C1

o

b C1B

C4B

C2B C3B

Supramolecular Structural Chemistry

751

a

Rosette layer

C10

Oxalate-water chain

Rosette layer C5 C9

c o

C8

C7 C6

b

chains derived from centrosymmetric oxalate C(10) and water molecules O1w and O2w via strong + N–H· · · O− hydrogen bonds to generate a complex three-dimensonal host framework, within which the second kind of disordered (C2 H5 )4 N+ ions are accommodated in a zigzag fashion within channels extending along the [010] direction. The predicted assembly of guanidinium-trimesate network II was achieved through the crystallization of [(C2 H5 )4 N+ ]2 · [C(NH2 )+ 3 ] · [1,3, 5-C3 H3 (COO− )3 ] · 6H2 O (2). The guanidinium and trimesate ions are connected together by pairs of strong charge-assisted + N–H· · · O− hydrogen bonds to generate an essentially planar rosette layer with large honeycomb cavities [Fig. 20.2.15 (left)]. Three independent water molecules constitute a cyclic (H2 O)6 cluster of symmetry 2, which is tightly fitted into each host cavity by adopting a flattened-chair configuration in an out-of-plane orientaion, with O· · · O distances comparable to 275.9 pm in deuterated ice Ih . Each water molecule has its ordered hydrogen atom pointing outward to form a strong O–H· · · O− hydrogen bond with a carboxylate oxygen on the inner rim of the cavity. The well-ordered (C2 H5 )4 N+ guests, represented by large spheres, are sandwiched between anionic rosette host layers with an interlayer spacing of ∼7.5 Å [Fig. 20.2.15 (right)].

Fig. 20.2.14.

Perspective view of the crystal structure of (1) along [001]. The undulating guanidinium-carbonate rosette network I appears as a sinusoidal cross section. Adjacent composite hydrogen-bonded layers are interconnected by a [C2 O2− 4 · (H2 O)2 ]∞ chain. The disordered oxalate is shown in one possible orientation, and the two different types of disordered Et4 N+ ions (represented by large semi-transparent spheres) are included in the pouches and the zigzag channels running parallel to the [010] direction, respectively.

752

Structural Chemistry of Selected Elements

c

C6

O

C3 O2

C4

C5

O2W O1

C1 N2

N1

b

O3

C2 O1W

O3W

O1WA

O3WA

O2WA

b

a

o

a

Fig. 20.2.15.

(Left) Projection diagram showing the hydrogen-bonding scheme in the infinite rosette layer II of (2). Only one of the two cyclic arrangements of disordered H atoms lying on the edges of each (H2 O)6 ring is displayed. Symmetry transformation: A (1 − x, y, 1 /2 − z). (Right) Sandwich-like crystal structure of (2) viewed along the b axis.

The malleability of guanidinium-carbonate network I, rendered possible by the prolific hydrogen-bond accepting capacity of its carbonate building block, opens up opportunities for further exploration of supramolecular assembly. The flattened-chair (H2 O)6 guest species, filling the cavity within robust guanidinium-trimesate layer II and being comparable to that in the host lattice of bimesityl-3,3, -dicarboxylic acid, may conceivably be replaced by appropriate hydrogen-bond donor molecules. The present anionic rosette networks are unlike previously reported neutral honeycomb lattices of the same (6,3) topology, thus expanding the scope of de novo engineering of charge-assisted hydrogen-bonded networks using ionic modular components, from which discrete molecular aggregates bearing the rosette motif may be derived. 20.3

Supramolecular chemistry of the coordination bond

The predictable coordination geometry of transition metals and the directional characteristics of interacting sites in a designed ligand provide the blueprint (or programmed instructions) for the rational synthesis of a wide variety of supramolecular inorganic and organometallic systems. Current research is concentrated in two major areas: (a) the construction of novel supermolecules from the intermolecular association of a few components and (b) the spontaneous organization (or self-assembly) of molecular units into one-, two-, and threedimensional arrays. In the solid state, the supermolecules and supramolecular arrays can further associate with one another to yield gigantic macroscopic conglomerates, i.e., supramolecular structures of higher order. 20.3.1

Principal types of supermolecules

The supermolecules that have been synthesized include large metallocyclic rings, helices, host–guest complexes, and interlocked structures such as catenanes, rotaxanes, and knots.

Supramolecular Structural Chemistry

[2]rotaxane

polyrotaxane

[2]catenane

753

polycatenane

Fig. 20.3.1.

molecular necklace

topomers of a trefoil knot

Borromean link

The simplest catenane is [2]catenane which contains two interlocked rings. A polycatenane has three or more rings interlocked in a one-to-one linear fashion. A rotaxane has a ring component (or a bead) threaded by a linear component (or a string) with a stopper at each end. A polyrotaxane has several rings threaded onto the same string. A molecular necklace is a cyclic oligorotaxane with several rings threaded by a closed loop. There are two topological isomers for a trefoil knot. The Borromean link is composed of three interlocked rings such that the scission of any one ring unlocks the other two. These topologies are shown in Fig. 20.3.1.

20.3.2

Some examples of inorganic supermolecules

(1) Ferric wheel The best known example of a large metallocyclic ring is the “ferric wheel” [Fe(OMe)2 (O2 CCH2 Cl)]10 prepared from the reaction of oxo-centered trinuclear [Fe3 O(O2 CCH2 Cl)6 (H2 O)3 ](NO3 ) and Fe(NO3 )3 ·9H2 O in methanol. An X-ray analysis showed that it is a decameric wheel having a diameter of about 1.2 nm with a small and unoccupied hole in the middle (Fig. 20.3.2). Each pair of iron(III) centers are bridged by two methoxides and one O, O, -chloroacetate group. (2) Hemicarceplex A carcerand is a closed-surface, globular host molecule with a hollow interior that can enclose guest species such as small organic molecules and inorganic ions to form a carceplex. A hemicarcerand is a carcerand that contains portals large enough for the imprisoned guest molecule to escape at high temperatures, but otherwise remains stable under normal laboratory conditions. The hemicarcerand host molecule designed by Cram shown in Fig. 20.3.3 has idealized D4h symmetry with its fourfold axis roughly coincident with the long axis of the ferrocene guest, which lies at an inversion center and hence adopts a fully staggered D5d conformation. The 1,3-diiminobenzene groups connecting the northern and southern hemispheres of the hemicarceplex are arranged like paddles in a paddle wheel around the circumference of the central cavity.

Catenanes, rotaxanes, molecular necklace, knots, and Borromean link.

754

Structural Chemistry of Selected Elements

Fe O C Cl Fig. 20.3.2.

Molecular structure of the ferric wheel.

(3) [2]Catenane Pt(II) complex The coordination bond between a pyridyl N atom and Pt(II) is normally quite stable, but it becomes labile in a highly polar medium at high concentration. Figure 20.3.4 shows the overall one-way transformation of a binuclear cyclic Pt(II) complex into a dimeric [2]catenane framework, which can be isolated as its nitrate salt upon cooling. R

R

H

O

O

O

HC

R

H

O

HC

O

N

N

R

H

H

CH

O

O

O

CH

N

N

Fe N

O

HC O

O

O

N

N

N

HC

CH

O

O

O

CH O

Fig. 20.3.3.

A hemicarceplex consisting of a hemicarcerand host molecule enclosing a ferrocene guest molecule.

H R

R

H

H

H R

R

(4) Helicate In a helicate the polytopic ligand winds around a linear array of metal ions lying on the helical axis, so that its ligation sites match the coordination requirements

Supramolecular Structural Chemistry NH2 H2N Pt N N

H2N N

Pt

755

NH2 N N

Pt

NH2 N

5M NaNO3 100 ºC, 24h

N N Pt NH2 H2N

N H2N

Pt

N N Pt N H2N NH2 NH2

(NO3)4

Fig. 20.3.4.

(NO3)8

Self-assembly of a [2]catenane Pt(II) complex.

of the metal centers. The two enantiomers of a helicate are designated P- for a right-handed helix and M - for a left-handed helix [Fig. 20.3.5(a)]. An example of a M -type Cu(I) double helicate is shown in Fig. 20.3.5(b). Double helicates containing up to five Cu(I) centers and triple helicates involving the wrapping of oligobidentate ligands around octahedral Co(II) and Ni(II) centers have been synthesized. helical axis ligation site

Cu

Cu Cu spacer Fig. 20.3.5.

oligobidentate ligand

(5) Molecular trefoil knot The first molecular trefoil knot was successfully synthesized by DietrichBuchecker and Sauvage according to the scheme shown in Fig. 20.3.6. A specially designed ligand consisting of two diphenolic 1,10-phenanthroline units tied together by a tetramethylene tether was reacted with [Cu(MeCN)4 ]BF4 to give a dinuclear double helix. This precursor was then treated under high dilution conditions with two equivalents of the diiodo derivative of hexaethylene glycol in the presence of Cs2 CO3 to form the cyclized complex in low yield. Finally, demetallation of this helical dicopper complex yielded the desired free trefoil knot with retention of topological chirality. It should be noted that in the crucial cyclization step, the double helical precursor is in equilibrium with a

(a) Structural features of a M -type helicate (only one strand is shown). (b) A Cu(I) double helicate containing an oligopyridine ligand.

756

Structural Chemistry of Selected Elements OH HO N

2

N

N

N

[Cu(CH3 CN)4]+

N

OH

N

N

N N

N N

HO

HO

N

OH

CsCO3, DMF, 60ºC ICH2(CH2OCH2)5 CH2I

O

O N

N

O O

O

O

O

N

N

N O

O

O

O

O O

O

O

N

N

O

O

O O

O

N

N

N

KCN

N N

N N

O

O

N

O

O

O O

O

O

Fig. 20.3.6.

Synthetic scheme for dicopper and free trefoil knots. From C. O. Dietrich-Buchecker, J. Guilhem, C. Pascard and J.-P. Sauvage, Angew. Chem. Int. Ed. 29, 1154–6 (1990).

non-helical species, which leads to an unknotted dicopper complex consisting of two 43-membered rings arranged around two Cu(I) centers in a face-to-face manner (Fig. 20.3.7). (6) Molecular Borromean link The connection between chemistry and topology is exemplified by the elegant construction of a molecular Borromean link that consists of three identical interlocked rings. In the designed synthesis, each component ring comprises two short and two long segments. The programmed, one-step self-assembly process is indicated by the scheme illustrated in Fig. 20.3.8. Self-assembly of the molecular Borromean link (a dodecacation BR12+ ) is achieved by a template-directed cooperative process that results in over 90% yield. Each of the three component rings (L) in BR12+ is constructed from [2+2] macrocyclization involving two DFP (2,6-diformylpyridine) and two DAB (diamine containing a 2,2, -bipyridyl group) molecules. Kinetically labile

Supramolecular Structural Chemistry

2

+2

cyclize

–2

cyclize

Fig. 20.3.7.

Template synthesis of a free trefoil knot and an unknotted product.

zinc(II) ions serve efficiently as templates in multiple molecular recognition that results in precise interlocking of three macrocyclic ligands: CH3 OH

6DFB + 6[DABH4 ](CF3 CO2 )4 + 9Zn(CF3 CO2 )2 −→ [L3 (ZnCF3 CO2 )6 ] · 3[Zn(CF3 CO2 )4 ] + 12H2 O |||

[BR(CF3 CO2 )6 ] · 3[Zn(CF3 CO2 )4 ] An X-ray analysis of [BR(CF3 CO2 )6 ]·3[Zn(CF3 CO2 )4 ] revealed that the hexacation [BR(CF3 CO2 )6 ]6+ has S6 symmetry with each macrocyclic ligand L adopting a chair-like conformation (Fig. 20.3.8). The interlocked rings are consolidated by six Zn(II) ions, each being coordinated in a slightly distorted octahedral geometry by the endo-tridentate diiminopyridyl group of one ring, the exo-bidentate bipyridyl group of another ring, and an oxygen atom of a CF3 CO− 2 ligand. Each bipyridyl group is sandwiched unsymmetrically between a pair of phenolic rings at π–π stacking distance of 361 and 366 pm in different directions. In the crystal packing, the [BR(CF3 CO2 )6 ]6+ ions are arranged in hexagonal arrays with intermolecular π–π stacking interactions of 331 pm and C–H· · · O=C hydrogen bonds (H· · · O 252 pm), generating columns along c that accommodate the [Zn(CF3 CO2 )4 ]2− counterions. 20.3.3

Synthetic strategies for inorganic supermolecules and coordination polymers

Two basic approaches for the synthesis of inorganic supermolecules and one-, two-, and three-dimensional coordination polymers have been developed:

757

758

Structural Chemistry of Selected Elements H

DFP (used in construction of short ring segment)

H

N O

O

N

N

DAB (used in construction of long ring segment)

O

O

NH2

H2N

H

H

N

NH2

N

N

N

Zn2+

H

N

O

–H2O

N

N

N O

O

NH2

N

N

H

H2 N

O

N O

O

O

N

N

N

H

N O

O

O

H

O H

H2 N

O N

H

BR12+ Fig. 20.3.8.

Synthetic scheme for one-step supramolecular assembly of the molecular Borromean link [L3 Zn6 ]12+ ≡ BR 12+ ; its three component interlocked rings are differentiated by different degrees of shading. Each octahedral zinc(II) ion is coordinated by an endo-N3 ligand set and a chelating bipyridyl group belonging to a different ring, the monodentate acetate ligand being omitted for clarity. From K. S. Chichak, S. J. Cantrill, A. R. Pease, S.-H. Chiu, G. W. V. Cave, J. L. Atwood and J. F. Stoddart, Science (Washington) 304, 1308–12 (2004).

(1) Transition-metal ions are employed as nodes and bifunctional ligands as spacers. Commonly used spacer ligands are pseudohalides such as cyanide, thiocyanate, and azide, and N-donor ligands such as pyrazine, 4,4, bipyridine, and 2,2, -bipyrimidine. Besides discrete supermolecules, some one-, two-, and three-dimensional architectural motifs generated from this strategy are shown in Fig. 20.3.9. If all nodes at the boundary of a portion of a motif are bound by terminal ligands, a discrete molecule will be formed. An example is the square grid shown in Fig. 20.3.10. Reaction of the tritopic ligand 6,6, bis[2-(6-methylpyridyl)]-3,3, -bipyridazine (Me2 bpbpz) with silver triflate in 2:3 molar ratio in nitromethane results in self-assembly of a complex of the formula [Ag9 (Me2 bpbpz)6 ](CF3 SO3 )9 . X-ray analysis showed that the [Ag9 (Me2 bpbpz)6 ]9+ cation is in the form of a 3 × 3 square grid, with two sets of Me2 bpbpz ligands positioned above and below the mean plane of the silver centers, as shown in Fig. 20.3.10(a), so that each Ag(I) atom is in a distorted tetrahedral environment. The grid is actually distorted into a diamond-like shape due to the curved nature of the ligand, and the

Supramolecular Structural Chemistry (a)

(b)

(c)

(d)

(e)

759 (g)

(f)

One-dimensional

(h)

(i)

(j)

(k)

(l)

Two-dimensional (m)

(n)

(o)

Three-dimensional Fig. 20.3.9.

Schematic representation of the motifs generated from the connection of transition metals by bifunctional spacer ligands. One-dimensional: (a) linear chain, (b) zigzag chain, (c) double chain, (d) helical chain, (e) fishbone, (f) ladder, and (g) railroad. Two-dimensional: (h) square grid, (i) honeycomb, (j) brick wall, (k) herringbone, and (l) bilayer. Three-dimensional: (m) six-connected network, (n) four-connected diamondoid network, and (o) four-connected ice-Ih network.

760

Structural Chemistry of Selected Elements

(a)

Me

(b)

N N N Ag N C

N Fig. 20.3.10.

N

The 3 × 3 square molecular grid [Ag9 (Me2 bpbpz)6 ]9+ : (a) structural formula and (b) molecular structure. From [P. N. W. Baxter, J-M. Lehn, J. Fischer and M-T. Youinou. Angew. Chem. Int. Ed. 33, 2284–7 (1994).

N Me

angle between the mean planes of the two sets of ligands is about 72◦ (Fig. 20.3.10(b)). (2) Exodentate multitopic ligands are used to link transition metal ions into building blocks. Some examples of such ligands are 2,4,6-tris(4pyridyl)-1,3,5-triazine, oligopyridines, and 3- and 4-pyridyl-substituted porphyrins. In the following sections, selected examples from the recent literature are used to illustrate the creative research activities in transition-metal supramolecular chemistry.

20.3.4

Molecular polygons and tubes

(1) Nickel wheel The reaction of hydrated nickel acetate with excess 6-chloro-2-pyridone (Hchp) produces in 60% yield a dodecanuclear nickel complex, which can be recrystallized from tetrahydrofuran as a solvate of stoichiometry [Ni12 (O2 CMe)12 (chp)12 (H2 O)6 (THF)6 ]. X-ray structure analysis revealed that this wheel-like molecule (Fig. 20.3.11) lies on a crystallographic threefold axis. There are two kinds of nickel atoms in distorted octahedral coordination: Ni(1) is bound to three O atoms from acetate groups, two O atoms from chp ligands, and an aqua ligand, whereas Ni(2) is surrounded by two acetate O atoms, two chp O atoms, an aqua ligand, and the terminal THF ligand. All ligands, other than THF, are involved in bridging pairs of adjacent nickel atoms. The structure of this nickel metallocycle resembles that of the decanuclear “ferric wheel” [Fe(OMe)2 (O2 CCH2 Cl)]10 (see Fig. 20.3.2). Both complexes feature a closed chain of intersecting M2 O2 rings, with each ring additionally bridged by an acetate ligand. They differ in that in the ferric wheel the carboxylate ligands are all exterior to the ring, whereas in the nickel wheel half of the acetate ligands lie within the central cavity.

Supramolecular Structural Chemistry

Cl

N H

O

Cl

N

761

OH

Hchp

Fig. 20.3.11.

Molecular structure of the nickel wheel. The bridging pyridone and terminal THF ligands point alternately above and below the mean plane of the twelve nickel atoms. From A. J. Blake, C. M. Grant, S. Parsons, J. M. Rawson and R. E. P. Winpenny. Chem. Commun., 2363–4 (1994).

(2) Nano-sized tubular section The ligand 2,4,6-tris[(4-pyridyl)methylsulfanyl]-1,3,5-triazine (tpst) possesses nine possible binding sites to transition metals for the assembly of supramolecular systems. Its reaction with AgNO3 in a 1:2 molar ratio in DMF/MeOH followed by addition of AgClO4 produces Ag7 (tpst)4 (ClO4 )2 (NO3 )5 (DMF)2 . In the crystal structure, two tpst ligands coordinate to three silver(I) ions to form a bicyclic ring. Two such rings are fitted together by Ag–N and Ag–S bonds involving a pair of bridging silver ions to generate a nano-sized tubular section [Ag7 (tpst)4 ] with dimensions of 1.34 × 0.96 × 0.89 nm, which encloses two perchlorate ions and two DMF molecules (Fig. 20.3.12). The tubular sections are further linked by additional Ag–N and Ag–S bonds to form an infinite chain. The nitrate ions are located near the silver ions and imbedded in between the linear polymers. The two independent tpst ligands are each bound to four silver atoms but in different coordination modes: three pyridyl N plus one thioether S, or three pyridyl N plus one triazine N. The silver atoms exhibit two kinds of coordination modes: normal linear AgN2 and a very unusual AgN2 S2 mode of distorted square-planar geometry. (3) Infinite square tube The reaction of 2-aminopyrimidine (apym), Na[N(CN)2 ], and M(NO3 )2 .6H2 O (M = Co, Ni) gives M[N(CN)2 ]2 (apym), which consists of a packing of infinite molecular tubes of square cross section. In each tube, the metal atoms constitute the edges and three connecting N(CN)− 2 (dicyanamide) ligands form the sides (Fig. 20.3.13). The octahedral coordination of the metal atoms is completed by chains of two-connecting ligands (with the amide nitrogen uncoordinated) which occupy the outside of each edge, as well as monodentate apym ligands. The length of a side of the molecular tube is 486.4 pm for M = Co and 482.1

762

Structural Chemistry of Selected Elements (a)

N Ag

Ag+

S N S

N

S

N

Ag+

N C S

N

N tpst

(b)

Fig. 20.3.12.

(a) Formation and structure of the nano-sized tubular section [Ag7 (tpst)4 ]. Bonds formed by bridging silver ions are indicated by broken lines. (b) Linkage of tubular sections to form a linear polymer. From M. Hong, Y. Zhao, W. Su, R. Cao, M. Fujita, Z. Zhou and A. S. C. Chan. Angew. Chem. Int. Ed. 39, 2468–70 (2000).

pm for M = Ni. In the crystal structure extensive hydrogen bonding between the tubes occurs via the terminal apym ligands.

N N

NH2

apym Fig. 20.3.13.

Structure of a square molecular tube in M[N(CN)2 ]2 (apym) (M=Co, Ni). From P. Jensen, S. R. Batten, B. Moubaraki and K. S. Murray, Chem. Commun., 793–4 (2000).

–N

C

20.3.5

N

C N

N

C

N

C

N–

Molecular polyhedra

(1) Tetrahedral iron(II) host–guest complex The structural unit M(tripod)n+ (tripod = CH3 C(CH2 PPh2 )3 ) has been used as a template for the construction of many supramolecular complexes. For example, the host–guest complex [BF4 ⊂ {(tripod)3 Fe}4 (transNCCH=CHCN)6 (BF4 )4 ](BF4 )3 has been synthesized from the reaction of tripod, Fe(BF4 )3 ·6H2 O, and fumaronitrile in a 4:4:6 molar ratio in CH2 Cl2 /EtOH at 20◦ C. The tetranuclear Fe(II) complex has idealized symmetry T , with a crystallographic twofold axis passing through the midpoints of a pair of edges of the Fe4 tetrahedron (Fig. 20.3.14). The B–F bonds of the encapsulated BF− 4 ion point toward the corner iron atoms. Each face of the Fe4 tetrahedron is

Supramolecular Structural Chemistry

763

P Fe N

F B

P N

Fe

Fe

capped by a BF− 4 group, and the remaining three are located in voids between the complex cations.

(2) Cubic molecular box The cyanometalate box {Cs ⊂ [Cp*Rh(CN)3 ]4 [Mo(CO)3 ]4 }3− is formed in low yield from the reaction of [Cp*Rh(CN)3 ]− (Cp* = C5 Me5 ) and (η6 -C6 H3 Me3 )Mo(CO)3 in the presence of cesium ions, and it can be crystallized as a Et4 N+ salt. The Cs+ ion serves as a template in the self-assembly of the anionic molecular box, which has a cubic Rh4 Mo4 (µ-CN)12 core with three exterior carbonyl ligands attached to each Mo and a Cp* group to each Rh. The encapsulated Cs+ ion has a formal coordination number of 12 if interaction with the centers of cyano groups is considered (Fig. 20.3.15).

(3) Lanthanum square antiprism A tris-bidentate pyrazolone ligand, 4-(1,3,5-benzenetricarbonyl)-tris(3-methyl1-phenyl-2-pyrazoline-5-one (H3 L), has been designed and synthesized. When this rigid C3 -symmetric ligand was reacted with La(acac)3 in dimethylsufoxide (DMSO), the complex La8 L8 (DMSO)24 was obtained in 81% yield. An X-ray analysis revealed a square-antiprismatic structure with idealized D4d symmetry, with each L3− ligand occupying one of the eight triangular faces (Fig. 20.3.16). In the coordination sphere of the La3+ ion, six sites are filled by O atoms from three L3− ligands and the remaining three by DMSO molecules which point into the central cavity. It was found that the DMSO ligands could be replaced partially by methanol in recrystallization.

Fig. 20.3.14.

Molecular structure of the tetrahedral Fe(II) host–guest complex cation. The capping BF− 4 groups and the phenyl rings of the tripod ligands have been omitted for clarity. From S. Mann, G. Huttner, L. Zsolnai and K. Heinze, Angew. Chem. Int. Ed. 35, 2808–9 (1996).

764

Structural Chemistry of Selected Elements

C

N O

Mo

Rh

Cs

Fig. 20.3.15.

Structure of the molecular cube that encloses a Cs+ ion. From K. K. Klausmeyer, S. R. Wilson and T. B. Rauchfuss. J. Am. Chem. Soc. 121, 2705–11 (1999).

CH3

Cl

O Cl

O

O

+ O

N

N CaO/dioxane N

Cl HO

O

La

OH O

N N

N

H3C

CH3

CH3 O

O N

N HO

N

La(acac)3/DMSO 100ºC

Fig. 20.3.16.

Synthesis and structure of the La8 L8 cluster. Only one L3− ligand is shown, and the coordinating DMSO moleclues have been omitted for clarity. From K. N. Raymond and J. Xu. Angew. Chem. Int. Ed. 39, 2745–7 (2000).

Supramolecular Structural Chemistry

S

765

P

O

Ag Fig. 20.3.17.

The super-adamantoid core of the 2+ cage. The [Ag6 (triphos)4 (CF3 SO− 3 )4 ] broken lines indicate one of the two adamantane cores formed by silver ions and triflate ligands, whose F atoms have been omitted for clarity. From S. L. James, D. M. P. Mingos, A. J. P. White and D. Williams, Chem Commun., 2323–4 (2000).

(4) Super-adamantoid cage A 2:3 molar mixture of MeC(CH2 PPh2 )3 (triphos) and silver triflate gives [Ag6 (triphos)4 (CF3 SO3 )4 ](CF3 SO3 )2 in high yield. The inorganic “superadamantoid” cage [Ag6 (triphos)4 (CF3 SO3 )4 ]2+ exhibiting approximate T molecular symmetry is formed with the CF3 SO− 3 ion as a template. In the cage structure (Fig. 20.3.17), an octahedron of silver(I) ions is bound by two sets of tritopic triphos and triflate ligands, each occupying four alternating faces of the octahedron. Thus six silver ions and four triphos ligands constitute one adamantane core, and likewise the silver ions and triflate ligands form a second adamantane core. A novel feature in this structure is the “endo-methyl” conformation of the triphos ligand, leaving only a small cavity at the center. (5) Chemical reaction in a coordination cage Flat panel-like ligands with multiple interacting sites have been used for metaldirected self-assembly of many fascinating supramolecular 3D structures. A simple triangular “molecular panel” is 2,4,6-tris(4-pyridyl)-1,3,5-triazine (L), which has been employed by Fujita to assemble a discrete [{Pt(bipy)}6 L4 ]12+ (bipy = 2,2, -bipyridine) coordination cage in quantitative yield by treating Pt(bipy)(NO3 )2 with L in a 3:2 molar ratio. In this complex cation, the Pt(II) atoms constitute an octahedron, and the triangular panels (L ligands) are located at four of the eight faces (Fig. 20.3.18). The Pt(bipy)2+ fragment thus serves as a cis-protected coordination block, each linking a pair of molecular panels. The nano-sized central cavity with a diameter of ∼1 nm is large enough to accommodate several guest molecules. Different types of guest species such as adamantane, adamantane carboxylate, o-carborane, and anisole have been used. In particular, C-shaped molecules such as cis-azobenzene and cis-stilbene derivatives can be encapsulated in the cavity as a dimer stabilized by the “phenyl-embrace” interaction.

766

Structural Chemistry of Selected Elements N N N

N

Pt

N

N N

N

L

Fig. 20.3.18.

Self-assembly of [{Pt(bipy)}6 L4 ]12+ cage.

Useful chemical reactions have been carried out in the nano-sized cavity, as illustrated by the in situ isolation of a labile cyclic siloxane trimer (Fig. 20.3.19). In the first step, three to four molecules of phenyltrimethoxysilane enter the cage and are hydrolyzed to siloxane molecules. Next, condensation takes place in the confined environment to generate the cyclic trimer {SiPh(OH)O–}3 , which is trapped and stabilized in a pure form. The overall reaction yields an inclusion complex [{SiPh(OH)O–}3 ⊂ {Pt(bipy)}6 L4 ](NO3 )12 ·7H2 O, which can be crystallized from aqueous solution in 92% yield. The all-cis configuration of the cyclic siloxane trimer and the structure of the inclusion complex have been determined by NMR and ESI-MS. (6) Nanoscale dodecahedron The dodecahedron is a Platonic solid that contains 12 fused pentagons formed from 20 vertices and 30 edges. An organic molecule of this exceptionally high icosahedral (Ih ) symmetry is the hydrocarbon dodecahedrane C20 H20 , which was first synthesized by Paquette in 1982. Recently an inorganic analog has been obtained from edge-directed self-assembly of a metallocyclic structure (Fig. 20.3.20) in a remarkably high 99% yield. The tridentate ligand at each vertex is tris(4, -pyridyl)methanol, and the linear bidentate subunit at each edge is bis[4,4, -(trans-Pt(PEt3 )2 (CF3 SO3 ))]benzene. The dodecahedral molecule carries 60 positive charges and encloses 60 CF3 SO− 3 anions, and its estimated diameter d along the threefold axis is about 5.5 nm. Using bis[4,4, -(trans-Pt(PPh3 )2 (CF3 SO3 ))]biphenyl as a longer linear linker, d for the resulting enlarged dodecahedron increases to about 7.5 nm.

Supramolecular Structural Chemistry

767

OMe n

Si OMe OMe

HO

OH OH Si l O Si O Si O

OH

+ D2O

n

Si OH

D2O

OH

Fig. 20.3.19.

Generation and stabilization of cyclic siloxane trimer in a self-assembled coordination cage. From M. Yoshizawa, T. Kusukawa, M. Fujita, and K. Yamaguchi. J. Am. Chem. Soc. 122, 6311–12, (2000).

OH

20

60+

N

N N

CH2Cl2, acetone OSO2CF3 R3P

Pt

PR3

60 30 n R3P

Pt

PR3

CF3SO3– endosed in cavity

R = Et, n = 1, D ~ 5.5 nm R = Ph, n = 2, D ~ 7.5 nm

OSO2CF3 Fig. 20.3.20.

Self-assembly of a nanoscale dodecahedron. The OH group attached to each quaternary C atom of the tris(4, -pyridyl)methanol molecule has been omitted for clarity. From B. Olenyuk, M. D. Levin, J. A. Whiteford, J. E. Shield and P. J. Stang, J. Am. Chem. Soc. 121, 10434–5 (2000).

768

Structural Chemistry of Selected Elements Mo Mn

N

C

Fig. 20.3.21.

The [Mn9 (µ-CN)30 Mo6 ] core of the high-spin cluster. From J. Larionova, M. Gross, M. Pilkington, H. Andres, H. Stoeckli-Evans, H. U. Güdel and S. Decurtins, Angew. Chem. Int. Ed. 39, 1605–9 (2000).

(7) High-spin rhombic dodecahedron The cluster [MnII {MnII (MeOH)3 }8 (µ-CN)30 {Mo(CN)3 }6 ]·5MeOH.2H2 O has a pentadecanuclear core of idealized Oh symmetry, as shown in Fig. 20.3.21. The nine Mn(II) ions constitute a body-centered cube, the six Mo(V) ions define an octahedron, and the two polyhedra interpenetrate each other so that the peripheral atoms exhibit the geometry of a rhombic dodecahedron. Each pair of adjacent metal centers is linked by a µ-cyano ligand with Mo bonded to C and Mn bonded to N. Each outer Mn(II) atom is surrounded by three methanol ligands, leading to octahedral coordination. Similarly, three terminal cyano ligands are bound to each Mo(V) to establish an eight-coordination environment. Actually the cluster has a lower symmetry with a crystallographic C2 axis passing through the central Mn atom and the midpoints of two opposite Mo· · · Mo edges. The resulting neutral cluster has a high-spin ground state with S = 251/2. [Note that S = 21/2 for Mn(II) and 1/2 for Mo(V); thus the total spin of the system is 9 × 21/2 + 6 × 1/2 = 251/2.] 20.4

Selected examples in crystal engineering

Examples from the recent literature that illustrate various approaches in the rational design of novel crystalline materials are given in this section. 20.4.1

Diamondoid networks

The three-dimensional network structure of diamond can be considered as constructed from the linkage of nodes (C atoms) with rods (C–C bonds) in a tetrahedral pattern. From the viewpoint of crystal engineering, in a diamondoid network the node can be any group with tetrahedral connectivity, and the linking rods (or linker) can be all kinds of bonding interactions (ionic, covalent, coordination, hydrogen bond, and weak interactions) or molecular fragment. The molecular skeletons of adamantane, (CH2 )6 (CH)4 , and hexamethylenetetramine, (CH2 )6 N4 (Fig. 20.4.1) constitute the characteristic structural units of diamondoid networks containing one and two kinds of four-connected nodes, respectively. If the rod is long, the resulting diamondoid network

Supramolecular Structural Chemistry (a)

769

(b)

Fig. 20.4.1.

Molecular structure of (a) adamantane and (b) hexamethylenetetramine.

becomes quite porous, and stability can only be achieved by interpenetration. If two diamondoid networks interpenetrate to form the crystal structure, the degree of interpenetration ρ is equal to 2. Examples in which ρ ranges from 2 to 9 are known. Some crystalline compounds that exhibit diamondoid structures are listed in Table 20.4.1. The rod linking a pair of nodes can be either linear or nonlinear. In the crystal structure of Cu2 O, each O atom is surrounded tetrahedrally by four Cu atoms, and each Cu atom is connected to two O atoms in a linear fashion. Hence the node is the O atom, and the rod is O–Cu–O. Figure 20.4.2 shows a single Cu2 O diamondoid network, and the crystal structure is composed of two interpenetrating networks. In the crystal structure of ice-VII, which is formed under high pressure, the node is the O atom, and the rod is a hydrogen bond. Since the H atoms are disordered, the hydrogen bond is written as O· · · H· · · O in Table 20.4.1, indicating equal population of O–H· · · O and O· · · H–O. The degree of interpenetration is two, as shown in Fig. 20.4.3. Figures 20.4.4(a) and 20.4.4(b) illustrate the crystal structure of the 1:1 complex of tetraphenylmethane and carbon tetrabromide. The nodes comprise C(C6 H5 )4 and CBr4 molecules, and the each linking rod is the weak interaction between a Br atom and a phenyl group. The hexamethylenetetramine-like structural unit is outlined by broken lines. Figures 20.4.4(c) and 20.4.4(d) show the crystal structure of tetrakis(4-bromophenyl)methane, which has a distorted diamondoid network based on the hexamethylenetetramine building unit. If the synthon composed of the aggregation of four Br atoms is considered as a node, then two kinds of nodes (Br4 synthon and quatenary C atom) are connected by rods consisting of p-phenylene moeities. Figure 20.4.5 shows the crystal structure of [Cu{1,4-C6 H4 (CN)2 }2 ]BF4 . The nodes are the four-connected Cu atoms, each being coordinated tetrahedrally by N≡C–C6 H4 –C≡N ligands as rods. The adamantane-like structure unit is shown in Fig. 20.4.5(a), and repetition of such units along a twofold axis leads to fivefold interpenetration. The remaining space is filled by the BF− 4 ions. Figure 20.4.6 shows the crystal structure of C(C6 H4 C2 C5 NH4 O)· 8C2 H5 COOH. The whole C(C6 H4 C2 C5 NH4 O)4 molecule serves as a node, and

770

Structural Chemistry of Selected Elements

Table 20.4.1. Diamondoid networks

Compound

Node

Linking rod

Bond type between nodes

Degree of interpenetration ρ

Diamond M2 O (M = Cu, Ag, Pb) Ice-VII

C O

C–C O–M–O

Covalent Ionic/covalent

None Two

O

O· · · H· · · O

H bond

Two

KH2 PO4

H2 PO− 4

O–H· · · O

H bond

Two

Methanetetraacetic acid

C(CH2 COOH)4

Cyclic dimeric H bond

Three

(CH2 )6 N4 ·CBr4

(CH2 )6 N4 , CBr4 C(C6 H5 )4 , CBr4

N· · · Br interaction Br· · · phenyl interaction

Two

Covalent

Three

C

O

H O

O H

C(C6 H5 )4 ·CBr4

O

C

N· · · Br

Br C–Br

Remarks

Fig. 20.4.2 H atom disordered Fig. 20.4.3 K+ in channel

Fig. 20.4.4(a) Fig. 20.4.4(b)

None

Tetrahedral Br4 synthon consolidated by weak Br· · · Br interaction Fig. 20.4.4(c) Fig. 20.4.4(d)

C(4-C6 H4 Br)4

C(C6 H4 )4 unit, Br4 synthon

M(CN)2 (M = Zn, Cd) [Cu(L)2 ]BF4 (L = p-C6 H4 (CN)2 ) C(C6 H4 C2 C5 NH4 O)4 ·8CH3 CH2 COOH

M

M←C≡N→M

Coordination

Two

Cu

Ag←NCC6 H4 CN→Ag

Coordination

Five

Double N–H· · · O

Seven

[Ag(L)2 ]XF6 (L = 4, 4, -NCC6 H4 – C6 H4 CN, X = P, As, Sb) [Ag(L)]BF4 · xPhNO2 (L = C(4-C6 H4 mCN )4 )

Ag

Cyclic dimeric H bond Coordination

BF− 4 in channel Fig. 20.4.5 Fig. 20.4.6

Nine

XF− 6 in channel

Coordination

None

BF− 4 and PhNO2 guest species in cavity

[Mn(CO)3 (µ-OH)]4 · (H2 NCH2 CH2 NH2)

[Mn(CO)3 –(µ-OH)]4

H bond

Three

C(C6 H4 C2 C5 NH4 O)4

Ag←NCC6 H4 − C6 H4 CN→Ag

Ag, C(4-C6 H4 CN)4

CN→Ag

O–H· · · NH2 CH2 – CH2 NH2 · ··H–O

(a)

Fig. 20.4.2.

Crystal structure of Cu2 O: (a) single diamondoid network and (b) two interpenetrating networks.

(b)

Supramolecular Structural Chemistry

771

Fig. 20.4.3.

(Left) Two interpenetrating networks in the crystal structure of ice-VII. (Right) Two views of an adamantane-like structural unit.

(a)

(b)

(c)

(d)

Fig. 20.4.4.

(a) Crystal structure and (b) diamondoid network of C(C6 H5 )4 ·CBr4 . (c) Crystal structure and (d) distorted diamondoid network of C(4-C6 H4 Br).

(a)

(b)

Fig. 20.4.5.

(a) Single diamond network of [Cu{1,4-C6 H4 (CN)2 }2 ] and (b) fivefold interpenetration in the crystal structure.

772

Structural Chemistry of Selected Elements O N

O

H

H N

H

H

N O

N

O

O N

H

H

N

O

Fig. 20.4.6.

Crystal structure of C(C6 H4 C2 C5 NH4 O)4 ·8CH3 CH2 COOH. The structure of the host molecule is shown in the upper right and the pairwise linkage of pyridone groups is shown at the lower right.

such nodes are connected by rods each comprising a pair of N–H· · · O hydrogen bonds between pyridine groups. As the resulting diamondoid network is quite open, sevenfold interpenetration occurs, and the remaining space is used to accommodate the ethanol guest molecules. In the crystal structure of [Ag{C(4-C6 H4 CN)4 }]BF4 ·xPhNO2 , the structural unit is of the hexamethylenetetramine type (Fig. 20.4.7). The nodes areAg atoms and C(4-C6 H4 CN)4 molecules, and the rods are CN→Ag coordination bonds. The void space is filled by the nitrobenzene guest molecules and BF− 4 ions. 20.4.2

Interlocked structures constructed from cucurbituril

Cucurbituril is a hexameric macrocyclic compound with the formula (C6 H6 N4 O2 )6 shaped like a pumpkin which belongs to the botanical family Cucurbitaceae. This macrocyclic cavitand has idealized symmetry D6h with a hydrophobic internal cavity of about 0.55 nm. The two portals, which are each laced by six hydrophilic carbonyl groups, have a diameter of 0.4 nm [Fig. 20.4.8(a)]. Like a molecular bead, cucurbituril can be threaded with a linear diammonium ion to form an inclusion complex [Fig. 20.4.8(b)]. This is stabilized by the fact that each protonated amino N atom forms hydrogen bonds to three of the

Supramolecular Structural Chemistry

773

Fig. 20.4.7.

Hexamethylenetetramine-like structure unit in the diamondoid network of [Ag{C(4-C6 H4 CN)4 }]BF4 .

six carbonyl groups at its adjacent portal. Since each rotaxane unit has two terminal pyridyl groups, it can serve as an exo-bidentate ligand to link up transition metals to form a polyrotaxane which may take the form of a linear coordination polymer, a zigzag polymer, a molecular necklace, or a puckered layer network [Fig. 20.4.8(c)]. The structures of the linear and zigzag polyrotaxane polymers are shown in Fig. 20.4.9. The two-dimensional network is constructed from the fusion of chair-like hexagons with Ag(I) ions at the corners and rotaxane units forming the edges. The nitrate ions lie above and below the puckered layer such that each Ag(I) ion is coordinated by three rotaxanes and a nitrate ion in a distorted tetrahedral geometry. In the crystal structure, two sets of parallel two-dimensional networks stacked in different directions make a dihedral angle of 69◦ , and they interpenetrate in such a way that a hexagon belonging to one set interlocks with four hexagons of the other set, and vice versa. The rotaxane building unit can be modified by replacing the 4-pyridyl group by another functional group such as 3-cyanobenzyl. When a rotaxane unit built in this way is treated with Tb(NO3 )3 under hydrothermal conditions, the cyano group is converted to the carboxylate group to generate a three-dimensional coordination polymeric network. The basic building block of the framework consists of a binuclear Tb3+ center and two types of rotaxane units: type I having bridging 3-phenylcarboxylate terminals and type II having chelating carboxylate terminals (Fig. 20.4.10). The binuclear terbium centers and type I rotaxanes form a two-dimensional layer. Stacked layers are further interconnected via type II rotaxanes to form a three-dimensional polyrotaxane network, which has an inclined α-polonium topology with the binuclear terbium centers behaving as six-connected nodes (Fig. 20.4.10). The void space in the crystal packing is filled by a free rotaxane − unit, NO− 3 and OH counter ions, and water molecules.

774

Structural Chemistry of Selected Elements O

O N

N N (a)

N

N

N

O N

N

O

N O N

O

N

N

N

N O

N

N N

O

O

O N

N

N

O

(b) N

N N N

N O

H2 N +

+ N H2

N

+ N

H2 N +

+ N H2

N

3+ Ag n

Ag

(CH

3C 6H 4 SO 3)

linear chain

NO 3

Ag

puckered layer

(c) ) O3 2

(N

Cu

O2NO

Cu OH2

zigzag chain

Pt

NH2

NH2

ONO2 n

Pt

H2N

4+

H2O

H2O

H2N

H2N

Pt NH2

Pt

NH2

H2N

molecular necklace

Fig. 20.4.8.

(a) Molecular structure of cucurbituril and its representation as a molecular bead or barrel, (b) cucurbituril threaded with a linear diammonium ion to form an inclusion complex, and (c) rotaxane building unit obtained by threading cucurbituril with diprotonated N,N, -bis(4-pyridylmethyl)-1,4-diaminobutane, and its subsequent reactions to yield linear polymers, a puckered layer, and a molecular triangle.

Supramolecular Structural Chemistry

775

(a)

(b)

Fig. 20.4.9.

Structure of (a) a linear polyrotaxane and (b) a zigzag polyrotaxane.

Type II

O1 O1W

O6

TbA O3 Tb O4 O5

N1

Type I

O2 O2W

N2

N3

Tb2 Fig. 20.4.10.

(a) Coordination geometry around the centrosymmetric binuclear terbium center. (b) Unit cell (top) and schematic representation (bottom) of the α-polonium-type network. Two contacting black circles stand for a binuclear terbium center, and the solid and open rods represent type I and type II rotaxane, respectively. From E. Lee, J. Heo and K. Kim, Angew. Chem. Int. Ed. 39, 2699–701 (2000).

776

Structural Chemistry of Selected Elements D H

D

H

H

L

A

M H

Fig. 20.4.11.

Domain model for hydrogen bonding involving metal complexes. Here D and A represent donor and acceptor atom, respectively. Note that both M–H and D–H units remain intact.

D

L

A

D

H

L A

A H

20.4.3

D

Inorganic crystal engineering using hydrogen bonds

The utilization of hydrogen bonding in inorganic crystal design has gained prominence in recent years. A conceptual framework for understanding supramolecular chemistry involving metals and metal complexes is provided by the domain model according to Dance and Brammer (Fig. 20.4.11). The central metal domain of a metal complex consists of the metal atom M, a metal hydride group, or a number of metal atoms if a metal cluster complex is considered. The ligand domain is composed of ligand atoms L directly bonded with the metal center(s). The periphery domain is the outmost part of the complex, consisting of those parts of the ligand not strongly influenced by electronic interaction with the metal center. Hydrogen bonding arising from donor groups (M)O–H and (M)N–H is commonly observed. The σ -type coordinated ligands are hydroxy (OH), aqua (OH2 ), alcohol (ROH), and amines (NH3 , NRH2 , NR2 H). Acceptors include halide-type (M–X with X = F, Cl, Br, I), hydride-type (D–H· · · H–M and D–H· · · H–E with E = B, Al, Ga) and carbonyl-type (D–H· · · OC–M). Some examples of the coordination polymers consolidated by hydrogen bonding are discussed below. (1) Chains In the crystal structure of Fe[η5 -CpCOOH]2 , a hydrogen-bonded chain with carboxyl groups interacting via the R22 (8) dimer synthon is formed [Fig. 20.4.12(a)]. The complex [Ag(nicotinamide)2 ]CF3 SO3 has a ladder structure propagated via the N–H· · · O catemer with rungs comprising R22 (8) amide dimer interactions [Fig. 20.4.12(b)]. Two CF3 SO− 3 ions (not shown) lie inside each centrosymmetric macrocyclic ring, and their O atoms form N–H· · · O–S–O· · · H–N hydrogen-bonded and weak Ag· · · O· · · Ag bridges. The crystal structure of [Ru(η5 -Cp)(η5 -1-p-tolyl-2-hydroxyindenyl)] features a zigzag chain linked by O–H· · · π(Cp) hydrogen bonds [Fig. 20.4.12(c)]. The crystal structures of [Pt(NCN–OH)Cl] and [Pt(SO2 )(NCN–OH)Cl], where NCN is the tridentate pincer ligand {C6 H2 -4-(OH)-2,6-(CH2 NMe2 )2 }− , are compared in Fig. 20.4.13. The colorless complex [Pt(NCN–OH)Cl]

Supramolecular Structural Chemistry

777

Fe O

H

C

(a)

N O Ag (b) T T

Ru

C

H O

(c)

T

T Fig. 20.4.12.

Hydrogen-bonded chain in (a) Fe[η5 -CpCOOH]2 , (b) [Ag(nicotinamide)2 ]+ , and (c) [Ru(η5 -Cp)(η5 -1-p-tolyl-2-hydroxyindenyl)] (T stands for p-tolyl group).

consists of a sheet-like array of parallel zigzag chains connected via O– H· · · Cl(Pt) hydrogen bonds. Reversible uptake of SO2 is accompanied by a color change, resulting in an orange complex [Pt(SO2 )(NCN–OH)Cl] in which the coordinated SO2 ligand is involved in a donor–acceptor S· · · Cl interaction. (2) Two-dimensional networks The O–H· · · O− hydrogen-bonded square grid found in [Pt(L2 )(HL)2 ]·2H2 O (HL = isonicotinic acid) is shown in Fig. 20.4.14(a). Water molecules (not shown) occupy channels in the threefold interpenetrated network. The crystal structure of [Zn(SC(NH2 )NHN H2 )2 (OH)2 ][1,4-O2 CC6 H4 CO2 ]·2H2 O has a brick-wall sheet structure [Fig. 20.4.14(b)]. Each N ,S-chelating thiosemicarbazide ligand forms two donor hydrogen bonds with one carboxylate group

778

Structural Chemistry of Selected Elements H

O Pt N

H S

Cl

N Pt

Cl

Fig. 20.4.13.

(a) Zigzag chain of [Pt(NCN–OH)Cl] held by O–H· · · Cl hydrogen bonds. (b) Two-dimensional network of [Pt(SO2 )(NCN–OH)Cl] consolidated by additional S· · · Cl donor–acceptor interactions.

of a terephthalate ion and one donor hydrogen bond with another terephthalate ion. The layers are linked via N–H· · · O and O–H· · · O hydrogen bonds to the water molecules (not shown). The complex [Ag(nicotinamide)2 ]PF6 has a cationic herringbone layer constructed from amide N–H· · · O hydrogen bonds [Fig. 20.4.14(c)]. Such layers are further cross-linked by N–H· · · F and C–H· · · F hydrogen bonds involving the PF− 6 ions (not shown). (3) Three-dimensional networks In the complex [Cu(L)4 ]PF6 (L = 3-cyano-6-methylpyrid-2(1H)-one), the hydrogen-bonded linkage involves the amido R22 (8) supramolecular synthon [Fig. 20.4.15(a)]. Each Cu(I) center serves as a tetrahedral node in a fourfold interpenetrated cationic diamondoid network. The tetrahedral metal cluster [Mn(µ3 -OH)(CO)3 ]4 can be used to construct a diamondoid network with the linear 4,4, -bipyridine spacers [Fig. 20.4.15(b)].

Supramolecular Structural Chemistry

Pt C

779

OH

N

(a)

N Zn S C

H O

(b)

Fig. 20.4.14.

C N (c)

Ag

O

(a) Square grid in [Pt(L2 )(HL)2 ]·2H2 O (HL = isonicotinic acid). (b) Brick-wall sheet in [Zn(thiosemicarbazide)(OH)2 ](terephthate)·2H2 (c) Cationic layer structure of [Ag(nicotinamide)2 ]PF6 .

780

Structural Chemistry of Selected Elements (a)

(b)

O Mn(CO)3 Cu N

O O H

N

N

H O

Fig. 20.4.15.

(a) Part of the cationic diamondoid network in [Cu(L)4 ]PF6 (L = pyridone ligand). (b) Molecular components and linkage mode of the diamondoid network in [Mn(µ3 -OH)(CO)3 ]4 ·2(bipy)·2CH3 CN.

20.4.4

Generation and stabilization of unstable inorganic/organic anions in urea/thiourea complexes

Urea, thiourea, or their derivatives are often employed as useful building blocks for supramolecular architectures because they contain amido functional group which can form moderately strong N–H· · · X hydrogen bonds with rather well-defined and predictable hydrogen-bonding patterns. Furthermore, in the presence of anions, the hydrogen bond is strengthened by two to three times (40 to 190 kJ mol−1 ) compared with the bond strength involving uncharged molecular species (10 to 65 kJ mol−1 ). Hence, making use of this kind of chargeassisted N–H· · · X− hydrogen bonding interactions and bulky tetraalkylammonium cations as guest templates, some unstable organic anions A− can be generated in situ and stabilized in urea/thiourea-anion host frameworks. A series of inclusion compounds of the type R4 N+A− · m(NH2 )2 CX (where X = O or S) with novel topological features has been characterized. (1) Dihydrogen borate As mentioned in Section 13.5.1, the transient species [BO(OH)2 ]− has been stabilized by hydrogen-bonding interactions with the nearest urea molecules in the host framework of the inclusion compound [(CH3 )4 N]+ [BO(OH)2 ]− ·2(NH2 )2 CO·H2 O. A perspective view of the crystal structure along the [010] direction is presented in Fig. 20.4.16. The host lattice consists of a parallel arrangement of unidirectional channels whose cross section has the shape of a peanut. The diameter of each spheroidal half is about 704 pm, and the separation between two opposite walls at the waist of the channel is about 585 pm. The well-ordered tetramethylammonium cations are accommodated in double columns within each channel.

Supramolecular Structural Chemistry

781

a

Fig. 20.4.16.

o b

c

(2) Allophanate and 3-thioallophanate Allophanate esters H2 NCONHCOOR are among the oldest organic compounds recorded in the literature. The parent allophanic acid, H2 NCONHCOOH, is not known in the free state, whereas inorganic allophanate salts are unstable and readily hydrolyzed by water to carbon dioxide, urea, and carbonate. However, the elusive allophanate anion can be generated in situ and stabilized in the following three inclusion compounds: [(CH3 )4 N]+ [NH2 CONHCO2 ]− ·5(NH2 )2 CO [(n-C3 H7 )4 N]+ [NH2 CONHCO2 ]− ·3(NH2 )2 CO [(CH3 )3 N+ CH2 CH2 OH][NH2 CONHCO2 ]− ·(NH2 )2 CO

A part of the host framework in [(CH3 )4 N]+ [NH2 CONHCO2 ]− ·5(NH2 )2 CO is shown in Fig. 20.4.17. Two neighboring allophanate anions are arranged in a head-to-tail fashion and bridged by a urea molecule with N–H· · · O and chargeassisted N–H· · · O− hydrogen bonds to generate a zigzag ribbon. This ribbon is further joined to another ribbon related to it by an inversion center via pairs of N–H· · · O− hydrogen bonds to form a double ribbon. The hitherto unknown 3-thioallophanate anion has been trapped in the host lattice of [(n-C4 H9 )4 N]+ [H2 NCSNHCO2 ]− ·(NH2 )2 CS. The cyclic structure and molecular dimensions of the allophanate and 3-thioallophanate ions are compared in Fig. 20.4.18.As expected, the C–O bond involved in intramolecular hydrogen bonding in the 3-thioallophanate anion is longer than that in the allophanate anion. (3) Valence tautomers of the rhodizonate dianion The rhodizonate dianion C6 O2− 6 (Fig. 20.4.19) is a member of a series of planar monocyclic oxocarbon dianions Cn O2− n (n = 3, deltate; n = 4, squarate; n = 5, croconate; n = 6; rhodizonate) which have been recognized as nonbenzenoid aromatic compounds. However, this six-membered ring species

Crystal structure of [(CH3 )4 N]+ [BO(OH)2 ]− ·2(NH2 )2 CO·H2 O showing the channels extending parallel to the b axis and the enclosed cations. Broken lines represent hydrogen bonds, and the atoms are shown as points for clarity. From Q. Li, F. Xue and T. C. W. Mak, Inorg. Chem. 38, 4142–5 (1999).

782

Structural Chemistry of Selected Elements

Fig. 20.4.17.

Part of the host framework in [(CH3 )4 N]+ [H2 NCONHCO2 ]− ·5(NH2 )2 CO showing the double ribbon constructed by allophanate anions and one of the independent urea molecules. From T. C. W. Mak, W.-H. Yip and Q. Li, J. Am. Chem. Soc. 117, 11995–6 (1995).

C

H

N

O

is not stable in aqueous solution as it readily undergoes oxidative ring contraction reaction to the croconate dianion, and the decomposition is catalyzed by alkalis. Recently, this relatively unstable species has been generated in situ and stabilized by hydrogen bonding in two novel inclusion compounds [(nC4 H9 )4 N+ ]2 C6 O2− 6 ·2(m-OHC6 H4 NHCONH2 )·2H2 O (Fig. 20.4.20) and [(nC4 H9 )4 N+ ]2 C6 O2− 6 ·2(NH2 CONHCH2 CH2 NHCONH2 )·3H2 O (Fig. 20.4.21), respectively. H

H . ... . .

N

..

123.9

132.1 124.0

Fig. 20.4.18.

O

Bond lengths (pm) of the (a) allophanate and (b) 3-thioallophanate anion. From C.-K. Lam, T.-L. Chan and T. C. W. Mak, CrystEngComm. 6, 290–2 (2004).

H

O

N

140.8

..

O 125.1

130.8 170.0

125.6 137.2

H . ... . .

N

123.7 135.5

S

O

N

H

H

(a)

(b)

142.5

O

2− + The measured dimensions of the C6 O2− 6 species in [(n-C4 H9 )4 N ]2 C6 O6 ·2(m-OHC6 H4 NHCONH2 )·2H2 O and [(n-C4 H9 )4 N+ ]2 C6 O2− 6 ·2(NH2 CON HCH2 CH2 NHCONH2 )·3H2 O nearly conform to idealized D6h and C2v molecular symmetry, corresponding to distinct valence tautomeric structures that manifest nonbenzenoid aromatic and enediolate character, respectively (Fig. 20.4.22). O O

O

Structural formulas of cyclic oxocarbon dianions.

deltate

O

O

2–

O

2– O

O

O

O

2–

2– Fig. 20.4.19.

O

O

O

O

squarate

O

O

croconate

O O

rhodizonate

Occurrence of the charge-localized structure of C6 O2− in [(n6 2− + C4 H9 )4 N ]2 C6 O6 ·2(NH2 CONHCH2 CH2 NHCONH2 )·3H2 O, as well as its

Supramolecular Structural Chemistry

783

c

Fig. 20.4.20.

Projection along the b axis showing extensive hydrogen-bonding interactions around the centrosymmetric rhodizonate dianion in the host lattice of [(n-C4 H9 )4 N+ ]2 C6 O2− 6 ·2(mOHC6 H4 NHCONH2 )·2H2 O. From C.-K. Lam and T. C. W. Mak, Angew. Chem. Int. Ed. 40, 3453–5 (2001).

o a

noticeable deviation from idealized C2v molecular symmetry, can be attributed to unequal hydrogen-bonding interaction with its two neighboring bisurea donors and a pair of water molecules (Fig. 20.4.21). a

Fig. 20.4.21.

o

Projection along the b axis showing the hydrogen-bonding interactions within the puckered rhodizonate-bisurea-water layer of [(nC4 H9 )4 N+ ]2 C6 O2− 6 ·2(NH2 CONHCH2 CH2 NHCONH2 )·3H2 O. From C.-K. Lam and T. C. W. Mak, Angew. Chem. Int. Ed. 40, 3453–5 (2001).

c

(4) Valence tautomers of the croconate dianion In the host lattice of [(n-C3 H7 )4 N+ ]2 C5 O2− 5 ·3(NH2 )2 CO·8H2 O, the croconate anion resides in a rather symmetrical hydrogen-bonding environment (Fig. 20.4.23) and thus its measured dimensions are consistent with its expected charge-delocalized D5h structure in the ground state, as shown in O

O 124.6

O

144.2

C

C 2–

C O

124.6

O

144.1

C

124.6

O 124.1

144.0

124.6

C

124.2

O

O

O

126.3 140.4

C

C 147.2

143.9

C

123.1

(a)

O-

C 144.5 C

146.2

C C

144.1

O (b)

126.8

O–

Fig. 20.4.22.

Bond lengths (pm) of (a) D6h (note that in this case the dianion is located at a site of symmetry) and (b) C2v valence tautomers of the rhodizonate dianion.

784

Structural Chemistry of Selected Elements Fig. 20.4.24(a). In the host lattice of [(C2 H5 )4 N+ ]2 C5 O2− 5 ·3(CH3 NH)2 CO, the croconate dianion resides on a twofold axis, being directly linked to three 1,3dimethylurea molecules through pairs of N–H· · · O hydrogen bonds to form a semi-circular structural unit (Fig. 20.4.25). In particular, each type O1 oxygen atom forms two strong acceptor hydrogen bonds with the N–H donors from a pair of 1,3-dimethylurea molecules, while each type O2 oxygen atom forms only one N–H· · · O hydrogen bond. In contrast, the solitary type O3 oxygen atom is stabilized by two weak C–H· · · O hydrogen bonds with neighboring tetra-nbutylammonium cations. Such a highly unsymmetrical environment engenders a sharp gradient of hydrogen-bonding donor strength around the croconate ion, which is conducive to stabilization of its C2v valence tautomer with significantly different C–C and C–O bond lengths around the cyclic system, as shown in Fig. 20.4.24(b).

o C

H N

C

D

E

DCEDCE...

A ABAB...

B

Fig. 20.4.23.

¯ plane showing the hydrogen-bonding scheme for a portion of the host lattice in Projection diagram on the (110) [(n-C3 H7 )4 N+ ]2 C5 O2− ·3(NH 2 )2 CO·8H2 O. The slanted vertical (urea dimer–croconate–urea)∞ chain constitutes a side wall of the [110] 5 channel system. The parallel [urea dimer–(H2 O)2 ]∞ ABAB… and [croconate–urea–(H2 O)4 ]∞ DCEDCE… ribbons define the channel system in the c direction. From C.-K. Lam, M.-F. Cheng, C.-L. Li J.-P. Zhang, X.-M. Chen, W.-K. Li and T. C. W. Mak, Chem. Commun., 448–9 (2004).

The examples given in this section show that crystal engineering provides a viable route to breaking the degeneracy of canonical forms of a molecular species, and an elusive anion can be generated in situ and stabilized in a crystalline inclusion compound through hydrogen-bonding interactions with neighboring hydrogen-bond donors, such as urea/thiourea or their derivatives, which can function as supramolecular stabilizing agents.

Supramolecular Structural Chemistry O

O

123.9

124.5 147.5

O

C

124.1

2– C

147.0

124.8

C O

146.9

C

C O

(a)

124.1

C

C

145.8

123.8

O

O

148.3

146.9

146.9

124.3

O

146.5

C

C

785

–O

(b)

C 125.7

O–

Fig. 20.4.24.

Bond lengths (pm) and angles (◦ ) of D5h (a) and C2v (b) valence tautomers of the croconate dianion.

Fig. 20.4.25.

Hydrogen-bonding environment of the croconate dianion in the crystal structure of [(C2 H5 )4 N+ ]2 C5 O2− 5 ·3(CH3 NH)2 CO.

20.4.5

Supramolecular assembly of silver(I) polyhedra with embedded acetylenediide dianion

Since 1998, a wide range of double, triple, and quadruple salts containingAg2 C2 (IUPAC name silver acetylenediide, commonly known as silver acetylide or silver carbide in the older literature) as a component have been synthesized and characterized (see Section 14.3.7 and the comprehensive review by Bruce and Low cited at the end of this chapter). Such Ag2 C2 -containing double, triple, and quadruple salts can be formulated as Ag2 C2 · nAgX, Ag2 C2 · mAgX·nAgY, and Ag2 C2 · lAgX·mAgY·nAgZ, respectively. The accumulated experimental data indicate that the acetylenediide dianion C2− 2 preferentially resides inside a silver(I) polyhedron of the type C2 @Agn (n = 6-10), which is jointly stabilized by ionic, covalent (σ , π, and mixed), and argentophilic interactions (see Section 19.6.2). However, the C2 @Agn cage is quite labile and its formation can be influenced by various factors such as solvent, reaction temperature, and the coexistence of anions, crown ethers, tetraaza macrocycles, organic cations, neutral ancillary ligands, and exo-bidentate bridging ligands, so that cage size and geometry are in general unpredictable.

786

Structural Chemistry of Selected Elements

(a)

(b)

(c)

Fig. 20.4.26.

(a) Crown-sandwiched structure of the discrete molecule in [Ag2 C2 ·5CF3 CO2Ag·2(15C5)·H2 O]·3H2 O. The F and H atoms have been omitted for clarity. (b) Space-filling drawing of the discrete supermolecule in [Ag14 (C2 )2 (CF3 CO2 )14 (dabcoH)4 (H2 O)1.5 ] · H2 O. (dabco = 1,4-diazabicyclo[2.2.2]octane). The trifluoroacetate and aqua ligands have been omitted for clarity. (c) Space-filling drawing of the discrete supermolecule [Ag8 (C2 )(CF3 CO2 )6 (L1 )6 ] viewed along its 3 symmetry axis (L1 = 4-hydroxyquinoline). The trifluoroacetate ligands have been omitted for clarity. From Q.-M. Wang and T. C. W. Mak, Angew. Chem. Int. Ed. 40, 1130–3 (2001); Q.-M. Wang and T. C. W. Mak, Inorg. Chem. 42, 1637–43 (2003); X.-L. Zhao, Q.-M. Wang and T. C. W. Mak, Inorg. Chem. 42, 7872–6 (2003).

(1) Discrete molecules To obtain discrete molecules, one effective strategy is to install protective cordons around the C2 @Agn moiety with neutral, multidentate ligands that can function as blocking groups or terminal stoppers. Small crown ethers have been introduced as structure-directing agents into the Ag2 C2 -containing system to prevent catenation and interlinkage of silver polyhedra. Judging from the rather poor host–guest complementarity of Ag(I) (soft cation) with a crown ether (hard O ligand sites), the latter is expected not to affect the formation of C2 @Agn , but to act as a capping ligand to an apex of the polyhedral silver cage. [Ag2 C2 ·5CF3 CO2Ag·2(15C5)·H2 O]·3H2 O (15C5 = [15]crown-5) can be obtained from an aqueous solution containing silver acetylenediide, silver trifluoroacetate, and 15C5. The discrete C2 @Ag7 moiety in [Ag2 C2 ·5CF3 CO2Ag·2(15C5)·H2 O]·3H2 O is a pentagonal bipyramid, with four equatorial edges bridged by CF3 CO− 2 groups while the two apical Ag atoms are each attached to a 15C5, as shown in Fig. 20.4.26(a). In this discrete molecule, one equatorial Ag atom is coordinated by a monodentate CF3 CO− 2 and the other by an aqua ligand. In [Ag14 (C2 )2 (CF3 CO2 )14 (dabcoH)4 (H2 O)1.5 ] · H2 O, the core is a Ag14 double cage constructed from edge-sharing of two triangulated dodecahedra. Apart from trifluoroacetate and aqua ligands, there are four monoprotonated dabco ligands surrounding the core unit, each being terminally coordinated to a silver(I) vertex, as shown in Fig. 20.4.26(b). For the discrete molecule [Ag8 (C2 )(CF3 CO2 )6 (L1 )6 ] (L1 = 4-hydroxyquinoline) of 3 symmetry displayed in Fig. 20.4.26(c), the encapsulated acetylenediide dianion in the rhombohedral Ag8 core is disordered about a crystallographic threefold axis that bisects the C≡C bond and passes through two opposite corners of the rhombohedron. Apart from the µ2 -O,O, trifluoroacetate

Supramolecular Structural Chemistry liagnds, there are six keto-L1 ligands surrounding the polynuclear core, each bridging an edge in the µ-O mode. In the structures shown in Fig. 20.4.26, the hydrophobic tails of perfluorocarboxylates, together with the bulky ancillary ligands, successfully prevent linkage between adjacent silver polyhedra, thus leading to discrete supermolecules. (2) Chains and columns Free betaines are zwitterions bearing a carboxylate group and a quaternary ammonium group, and the prototype of this series is the trimethylammonio derivative commonly called betaine (Me3 N+ CH2 COO− , IUPAC name trimethylammonioacetate, hereafter abbreviated as Me3 bet). Owing to their permanent bipolarity and overall charge neutrality, betaine and its derivatives (considered as carboxylate-type ligands) have distinct advantages over most carboxylates as ligands in the formation of coordination polymers: (1) synthetic access to water-soluble metal carboxylates; (2) generation of new structural varieties, such as complexes with metal centers bearing additional anionic ligands, and those with variable metal to carboxylate molar ratios; and (3) easy synthetic modification of ligand property by varying the substituents on the quaternary nitrogen atom or the backbone between the two polar terminals. The introduction of such ligands into the Ag2 C2 -containing system has led to isolation of supramolecular complexes showing chain-like or columnar structures. [(Ag2 C2 )2 (AgCF3 CO2 )9 (L2 )3 ] has a columnar structure composed of fused silver(I) double cages: a triangulated dodecahedron and a bicapped trigonal prism, each encapsulating an acetylenediide dianion. Such a neutral column is coated by a hydrophobic sheath composed of trifluoroacetate and L2 ligands, as shown in Fig. 20.4.27(a). The core in [(Ag2 C2 )2 (AgCF3 CO2 )10 (L3 )3 ]·H2 O is a double cage generated from edge-sharing of a square-antiprism and a distorted bicapped trigonalprism, with each single cage encapsulating an acetylenediide dianion. Double cages of this type are fused together to form a helical column, which is surrounded by a hydrophobic sheath composed of trifluoroacetate and L3 ligands, as shown in Fig. 20.4.27(b). The building unit in [(Ag2 C2 )(AgC2 F5 CO2 )6 (L4 )2 ] is a centrosymmetric double cage, in which each half encapsulates an acetylenediide dianion. Each single cage is an irregular monocapped trigonal prism with one appended atom. The L4 ligand acting in the µ2 -O, O, coordination mode links a pair of double cages to form an infinite chain, as shown in Fig. 20.4.27(c). In [(Ag2 C2 )(AgCF3 CO2 )7 (L5 )2 (H2 O)], the basic building unit is a distorted monocapped cube. The trifluoroacetate and L5 ligands act as µ3 -bridges across adjacent single cage blocks to form a bead-like chain [Fig, 20.4.27(d)]. (3) Two-dimensional structures The incorporation of ancillary N , N , - and N ,O-donor ligands into the Ag2 C2 containing system has led to a series of two-dimensional structures.

787

788

Structural Chemistry of Selected Elements

(a)

(b)

H3C

(c)

H3C

CH3

(d)

C2H5

CH3

+N

+N

N+

CH3

CH3 O

O–

O L2

L3

C2H5

O

O

O–

C2H5

+N

O–

–

O

L4

L5

Fig. 20.4.27.

2 (a) Projection along an infinite silver(I) column with enclosed C2− 2 species and hydrophobic sheath in [(Ag2 C2 )2 (AgCF3 CO2 )9 (L )3 ]. (b)

Perspective view of the infinite silver(I) helical column with C2− 2 species embedded in its inner core and an exterior coat comprising anionic and zwitterionic carboxylates in [(Ag2 C2 )2 (AgCF3 CO2 )10 (L3 )3 ]·H2 O. (c) Infinite chain generated from the linkage of (C2 )2 @Ag16 double cages by µ2 − O,O, L4 ligands in [(Ag2 C2 )(AgC2 F5 CO2 )6 (L4 )2 ]. (d) Infinite chain constructed from C2 @Ag9 polyhedra connected by L5 and trifluoroacetate bridges in [(Ag2 C2 )(AgCF3 CO2 )7 (L5 )2 (H2 O)]. From X.-L. Zhao, Q-M, Wang and T. C. W. Mak, Chem. Eur. J. 11, 2094–102 (2005).

In the synthesis of [(Ag2 C2 )(AgCF3 CO2 )4 (L6 )(H2 O)]·H2 O under hydrothermal reaction condition, the starting ligand 4-cyanopyridine undergoes hydrolysis to form 4-pyridine-carboxamide (L6 ). The basic building unit is a C2 @Ag8 single cage in the shape of a distorted triangulated dodecahedron. Such dodecahedra share edges to form a zigzag composite chain, which are further linked via L6 to generate a two-dimensional network Fig. 20.4.28(a). The L1 ligand, H3 O+ species, and the anionic polymeric system {[Ag11 (C2 )2 (C2 F5 CO2 )9 (H2 O)2 ]2− }∞ comprise (L1 ·H3 O)2 [Ag11 (C2 )2 (C2 F5 CO2 )9 (H2 O)2 ]·H2 O. The basic building unit in the latter is a Ag12 double cage composed of two irregular monocapped trigonal antiprisms sharing an edge. The double cages are fused together to generate an infinite, sinuous anionic column. The oxygen atoms of L1 and the water molecule are bridged by a proton to give the cationic aggregate L1 ·H3 O+ , which links the columns into a layer structure via hydrogen bonds with the pentafluoropropionate groups (Fig. 20.4.28(b)). [Ag8 (C2 )(CF3 CO2 )8 (H2 O)2 ]·(H2 O)4 ·(L7 H2 ) represents a rare example of a hydrogen-bonded layer-type host structure containing C2 @Agn that features

Supramolecular Structural Chemistry

789

the inclusion of organic guest species. The core is a centrosymmetric C2 @Ag8 single cage in the shape of a slightly distorted cube. The trifluoroacetate ligands functioning in the µ3 -coordination mode further interlink the single cages into an infinite zigzag silver(I) chain. Of the three independent water molecules, one forms an acceptor hydrogen bond with a terminal of the L7 H2 dication, the other serves as an aqua ligand bonded to a silver atom, and the third lying on a two fold axis functions as a bridge between aqua ligands belonging to adjacent silver(I) chains. The centrosymmetric L7 H2 ions each hydrogen-bonded to a pair of terminal water molecules are accommodated between adjacent layers, forming an inclusion complex, as shown in Fig. 20.4.28(c). (4) Three-dimensional structures The strategy of using C2 @Agn polyhedra as building blocks for the assembly of new coordination frameworks via introduction of potentially exo-bidentate nitrogen/oxygen-donor bridging ligands between agglomerated components has led to the isolation of three-dimensional supramolecular complexes exhibiting interesting crystal structures. In (Ag2 C2 )(AgCF3 CO2 )8 (L8 )2 (H2 O)4 , square-antiprismatic C2 @Ag8 cores are linked by trifluoroacetate groups to generate a columnar structure. Hydrogen bonds with the amino group of L8 and aqua ligands serving as donors and the oxygen atoms of the trifluoroacetate group as acceptors further connect the columns into a three-dimensional scaffold [Fig. 20.4.29(a)]. (a)

(b)

CONH2 L1

N

L6 Fig. 20.4.28.

(c)

OH N

N

N

L1

L7

(a) Ball-and-stick drawing of the two-dimensional structure in [(Ag2 C2 )(AgCF3 CO2 )4 (L6 )(H2 O)]·H2 O. (b) Schematic showing of the layer structure in (L1 ·H3 O)2 [Ag11 (C2 )2 (C2 F5 CO2 )9 (H2 O)2 ]·H2 O. (c) Two-dimensional host layer structure of [Ag8 (C2 )(CF3 CO2 )8 (H2 O)2 ]·(H2 O)4 ·(L7 H2 ) constructed from hydrogen bonds linking the silver(I) chains, with hydrogen-bonded (bpeH2 ·2H2 O)2+ moieties being accommodated between the host layers. From X.-L. Zhao and T. C. W. Mak, Dalton Trans., 3212–7 (2004); X.-L. Zhao, Q.-M. Wang and T. C. W. Mak, Inorg. Chem., 42, 7872–6 (2003); X.-L. Zhao, and T. C. W. Mak, Polyhedron 24, 940–8 (2005).

790

Structural Chemistry of Selected Elements

(a)

(b)

(c)

CONH2 HN

N

O N

C OH

N (L8)

(L9)

(L10)

Fig. 20.4.29.

(a) Three-dimensional architecture of (Ag2 C2 )(AgCF3 CO2 )8 (L8 )2 (H2 O)4 resulting from the linkage of silver columns via hydrogen bonds. (b) Three-dimensional architecture in (L9 H)3 ·[Ag8 (C2 )(CF3 CO2 )9 ]·H2 O generated from covalent silver chains linked by hydrogen bonds. (c) The (3,6) covalent network in [Ag7 (C2 )(CF3 CO2 )2 (L10 )3 ] constructed by the linkage of L10 with silver(I) columns. From X.-L.Zhao and T. C. W. Mak, Dalton Trans. 3212-7 (2004); X.-L. Zhao and T. C. W. Mak, Polyhedron 25, 975–82 (2006).

The building block in (L9 H)3 ·[Ag8 (C2 )(CF3 CO2 )9 ]·H2 O is a C2 @Ag8 single cage in the shape of triangulated dodecahedron located on a twofold axis. Silver cages of such type are connected by µ3 −O,O,O, trifluoroacetate ligands to form a zigzag anionic silver(I) column along the adirection. All three independent L9 molecules are protonated to satisfy the overall charge balance in the crystal structure. Notably, the resulting L9 H cations play a key role in the construction of the three-dimensional architecture. As shown in Fig. 20.4.29(b), the silver(I) columns are interconnected by hydrogen bonding with the protonated L9 serving as donors and O, F atoms of trifluoroacetate ligands as acceptors to form the three-dimensional network. In [Ag7 (C2 )(CF3 CO2 )2 (L10 )3 ], the basic building block is a centrosymmetric (C2 )2 @Ag14 double cage, with each half taking the shape of a distorted bicapped trigonal prism. Such double cages are fused together to form an infinite column. Each silver(I) column is linked to six other radiative silver(I) columns via L10 , and every three neighboring silver columns encircle a triangular hole, thus resulting in a (3,6) (or 36 ) topology, as displayed in Fig. 20.4.29(c). (5) Mixed-valent silver(I,II) compounds containing Ag2 C2 To investigate the effect of coexisting metal ions on the assembly of polyhedral silver(I) cages, macrocyclic N -donor ligand 1,4,8,11-tetramethyl1,4,8,11-tetraazacyclotetradecane (tmc) has been used for in situ generation

Supramolecular Structural Chemistry of [AgII (tmc)]. Mixed-valent silver complexes [AgII (tmc)(BF4 )][AgI6 (C2 ) (CF3 CO2 )5 (H2 O)]· H2 O and [AgII (tmc)][AgII (tmc)(H2 O)]2 [AgI11 (C2 ) (CF3 CO2 )12 (H2 O)4 ]2 have been isolated and structurally characterized. In [AgII (tmc)(BF4 )][AgI6 (C2 )(CF3 CO2 )5 (H2 O)]· H2 O, the addition of tmc leads to disproportionation of silver(I) to give elemental silver and complexed silver(II), the latter being stabilized by tmc to form [AgII (tmc)]2+ . Weak axial interactions of the d9 silver(II) center with adjacent BF4 − serve to link the complexed Ag(II) cations into a [AgII (tmc)(BF4 )]+1 ∞ column, which further induces the assembly of a novel anionic zigzag chain constructed from edgesharing of silver(I) triangulated dodecahedra, each enclosing a C2− 2 species (Fig. 20.4.30(a)). In [AgII (tmc)][AgII (tmc)(H2 O)]2 [AgI11 (C2 )(CF3 CO2 )12 (H2 O)4 ]2 , which lacks the participation of BF− 4 ions, the cations do not line up in a one-dimensional array and instead a dimeric supramolecular cluster anion is generated [Fig. 20.4.30(b)]. (6) Ligand-induced disruption of polyhedral C2 @Agn cage assembly Attempts to interfere with the assembly process to open the C2 @Agn cage or construct a large single cage for holding two or more C2− 2 species were carried out via the incorporation of the multidentate ligand pyzCONH2 (pyrazine-2carboxamide) into the reaction system. Pyrazine-2-carboxamide was selected as a structure-directing component by virtue of its very short spacer length and chelating capacity, and the introduction of the amide functionality could conceivably disrupt the assembly of C2 @Agn via the formation of hydrogen bonds. The ensuing study yielded two silver(I) complexes Ag12 (C2 )2 (CF3 CO2 )8 (2pyzCONH2 )3 and Ag20 (C2 )4 (C2 F5 CO2 )8 (2-pyzCOO)4 (2-pyzCONH2 )(H2 O)2 exhibiting novel C2 @Agn motifs. The basic structural unit of Ag12 (C2 )2 (CF3 CO2 )8 (2-pyzCONH2 )3 comprises the fusion of a distorted triangulated dodecahedral Ag8 cage containdianion and an open fish-like Ag6 (µ6 -C2 ) motif ing an embedded C2− 2 (a)

Fig. 20.4.30.

(b)

(a) Crystal structure of [AgII (tmc)(BF4 )][AgI6 (C2 )(CF3 CO2 )5 (H2 O)]· H2 O. (b) Perspective view of the structure of the dimeric supramolecular anion in [AgII (tmc)][AgII (tmc)(H2 O)]2 [AgI11 (C2 )(CF3 CO2 )12 (H2 O)4 ]2 . The F atoms of the CF3 CO− 2 ligands and some CF3 CO2 are omitted for clarity. From Q.-M. Wang and T. C. W. Mak, Chem. Commun., 807-8 (2001); Q.-M. Wang, H. K. Lee and T. C. W. Mak, New J. Chem. 26, 513-5 (2002).

791

792

Structural Chemistry of Selected Elements (a)

(b)

(c)

Fig. 20.4.31.

(a) Basic building unit in Ag12 (C2 )2 (CF3 CO2 )8 (2-pyzCONH2 )3 . (b) Open fish-like Ag6 (µ6 -C2 ) motif coordinated by four pyrazine-2-carboxamide ligands in Ag12 (C2 )2 (CF3 CO2 )8 (2-pyzCONH2 )3 . (c) The (C2 )2 @Ag13 in Ag20 (C2 )4 (C2 F5 CO2 )8 (2-pyzCOO)4 (2-pyzCONH2 )(H2 O)2 . From X.-L. Zhao and T. C. W. Mak, Organometallics 24, 4497–9 (2005).

[Fig. 20.4.31(a)]. In the Ag6 (µ6 -C2 ) motif, one carbon atom is embraced by four silver atoms in a butterfly arrangement and the other bonds to two silver atoms. Its existence can be rationalized by the fact that it is stabilized by four surrounding pyrazine-2-carboxamide ligands so that steric overcrowding obstructs the aggregation of silver(I) into a closed cage [Fig. 20.4.31(b)]. The basic building block in Ag20 (C2 )4 (C2 F5 CO2 )8 (2-pyz COO)4 (2-pyzCONH2 )(H2 O)2 is an aggregate composed of three polyhedral units: an unprecedented partially opened cage (C2 )2 @Ag13 [Fig.20.4.31(c)] and two similar distorted C2 @Ag6 trigonal prisms. A pair of C2− 2 dianions are completely encapsulated in the Ag13 cage. For simplicity, this single cage can be visualized as composed of two distorted cubes sharing a common face, with cleavage of four of the edges and capping of a lateral face. The two embedded C2− 2 dianions retain their triple-bond character with similar C–C bond lengths of 118(2) pm.

20.4.6

Supramolecular assembly with the silver(I)-ethynide synthon

In 2004, the silver carbide (Ag2 C4 ) was synthesized as a light gray powder, which behaves like its lower homologue Ag2 C2 , being insoluble in most solvents and highly explosive in the dry state when subjected to heating or mechanical shock. Using Ag2 C4 and the crude polymeric silver ethynide complexes [R–(C≡CAg)m ]∞ (R = aryl; m = 1 or 2) as starting materials, a variety of double and triple silver(I) salts containing 1,3-butadiynediide and related carbon-rich ethynide ligands have been synthesized. Investigation of the coordination modes of the ethynide moiety in these compounds led to the recognition of a new class of supramolecular synthons R–C≡C⊃Agn (n = 4, 5), which can be utilized to assemble a series of one-, two-, and three-dimensional networks together with argentophilic interactions, π–π stacking, silver-aromatic interactions and hydrogen bonding.

Supramolecular Structural Chemistry (a) Ag3

Ag4

(b)

Ag2A

C2A C1A Ag2

(c)

Ag4

Ag3A

Ag6

C1 C2

Ag2

Ag3

(e) Ag2E C2A C1A

Ag2 C1 C2 Ag2C Ag2B

Ag2G Ag2 Ag2F

Ag2D

Ag3A

C3A C4A Ag4A

C4 C3

Ag3

C2A C1A

Ag1

Ag4A

(d) Ag2A

Ag6A

Ag5 Ag1A

C1 C2

Ag1

793

Ag4

Ag5A

Ag2

Ag5

(f) Ag6

Ag3

Ag7 C3

C1

C4

C2 Ag1 Ag4

Ag4 C1 C2 C3

Ag5

C4

Ag8

Ag3 Ag8

Fig. 20.4.32.

Ag7

Ag1

Ag6

Observed µ8 -coordination modes of C2− 4 dianion. (a) Symmetrical mode with two butterfly-shaped baskets in Ag2 C4 ·6AgNO3 · nH2 O (n = 2, 3). From L. Zhao and T. C. W. Mak, J. Am. Chem. Soc. 126, 6852-3 (2004). (b) Symmetrical mode only with Ag−C σ bonds in Ag2 C4 ·16AgC2 F5 CO2 ·6CH3 CN·8H2 O. (c) Barb-like µ8 -coordination mode with two linearly coordinated C≡C−Ag bonds in triple salt Ag2 C4 ·AgF·3AgNO3 · 0.5H2 O. (d) Symmetrical mode with two parallel planar Ag4 aggregates in Ag2 C4 · 16AgC2 F5 CO2 ·24H2 O. (e) Unsymmetrical µ8 -coordination mode with one butterfly-shaped Ag4 basket and one planar Ag4 aggregate in Ag2 C4 ·6AgCF3 CO2 ·7H2 O. (f) Unsymmetrical µ8 -coordination mode with two butterfly-shaped Ag4 baskets in quadruple salt Ag2 C4 ·4AgNO3 ·Ag3 PO4 · AgPF2 O2 .

(1) Silver(I) complexes containing the C2− 4 dianion In all of its silver(I) complexes, the linear − C≡C–C≡C− dianion exhibits an unprecedented µ8 -coordination mode, each terminal being capped by four silver(I) atoms (Fig. 20.4.32). However, the σ - and π-type silver–ethynide interactions play different roles in symmetrical and unsymmetrical µ8 -coordination. Furthermore, coexisting ancillary anionic ligands, nitrile groups, and aqua molecules also influence the coordination environment around each terminal ethynide, which takes the form of a butterfly-shaped, barb-like, or planar Ag4 basket. The carbon–carbon triple- and single-bond lengths in C2− 4 are in good agreement with those observed in transition-metal 1,3-butadiyne-1,4-diyl complexes. The Ag· · · Ag distances within the Ag4 baskets are all shorter than 340 pm, suggesting the existence of significant Ag· · · Ag interactions. The [Ag4 C4Ag4 ] aggregates vide supra can be further linked by other anionic ligands such as nitrate and perfluorocarboxylate groups, and/or water molecules, to produce various two- or three-dimensional coordination networks. In the structure of Ag2 C4 · 6AgNO3 · 2H2 O, the [Ag4 C4Ag4 ] aggregates arranged in a pseudo-hexagonal array are connected by one nitrate group acting in the µ3 -O,O, ,O,, plus O,O, -chelating mode to form a thick layer normal to [100] [Fig. 20.4.33(a)]. Linkage of adjacent layers by the remaining two independent nitrate groups, abetted by O–H· · · O(nitrate) hydrogen bonding involving the aqua ligand, then generates a three-dimensional network. In the crystal structure of Ag2 C4 ·16AgC2 F5 CO2 ·24H2 O, each [Ag4 C4Ag4 ] unit connects with eight such units by eight [Ag2 (µ-O2 CC2 F5 )4 ] bridging ligands to form a (4,4) coordination network [Fig. 20.4.33(b)]. Through the

794 (a)

Structural Chemistry of Selected Elements (b)

(c)

(d)

Fig. 20.4.33.

Some examples of two- and three-dimensional coordination networks of Ag2 C4 : (a) pseudohexagonal array of [Ag4 C4Ag4 ] aggregates linked by an independent nitrate group in Ag2 C4 ·6AgNO3 ·2H2 O: (b) (4,4) network in ab plane of Ag2 C4 ·16AgC2 F5 CO2 ·24H2 O, which is composed of [Ag4 C4Ag4 ] aggregates connected by bridging [Ag2 (µ-O2 CC2 F5 )4 ] groups: (c) three-dimensional coordination network in Ag2 C4 ·AgF·3AgNO3 ·0.5H2 O through the coordination of µ3 -fluoride ligands, (d) Rosette layer in Ag2 C4 ·10AgCF3 CO2 ·2[(Et4 N)CF3 CO2 ] ·4(CH3 )3 CCN composed of [Ag4 C4Ag4 ] aggregates linked by one external silver atom and two trifluoroacetate groups.

linkage of the C4 carbon chains perpendicular to this network, an infinite channel is aligned along the [001] direction, and each accommodates a large number of pentafluoroethyl groups. In the crystal structure of Ag2 C4 ·AgF·3AgNO3 ·0.5H2 O, [Ag4 C4Ag4 ] aggregates are mutually connected through the linkage of nitrate groups and sharing of some silver atoms to form a silver column. The fluoride ions bridge these silver columns in the µ3 -mode to produce a structurally robust three-dimensional coordination network [(Fig. 20.4.33(c)]). With an external silver atom and two carboxylato oxygen atoms as bridging groups, the [Ag4 C4Ag4 ] aggregates in Ag2 C4 ·10AgCF3 CO2 ·2[(Et4 N)CF3 CO2 ]·4(CH3 )3 CCN are linked to form a two-dimensional rosette layer, in which the C2− 4 dianion acts as the shared border of two metallacycles [Fig. 20.4.33(d)]. (2)

Silver(I) complexes of isomeric phenylenediethynides with the supramolecular synthons Agn ⊂ C2 −x-C6 H4 −C2 ⊃Agn (x = p, m, o; n = 4, 5) The above study of silver(I) 1,3-butadiynediide complexes suggests that the Ag4 ⊂C2 −R−C2 ⊃Ag4 moiety may be conceived as a synthon for the assembly of coordination networks, by analogy to the plethora of wellknown supramolecular synthons that involve hydrogen bonding and other weak intermolecular interactions (see Section 20.1.5). With reference to 1,3butadiynediide as a standard, the p-phenylene ring was introduced as the bridging R group in the supramolecular synthon Agn ⊂C2 −R−C2 ⊃Agn with a lengthened linear π-conjugated backbone, and the aromatic ring of the resulting p-phenylenediethynide dianion could presumably partake in π–π stacking and silver–aromatic interaction. The isomeric m- and o-phenylenediethynides were also investigated in order to probe the influence of varying the relative orientation of the pair of terminal ethynide groups. In 2[Ag2 (p-C≡CC6 H4 C≡C)]·11AgCF3 CO2 ·4CH3 CN·2CH3 CH2 CN, the pphenylenediethynide ligand exhibits the highest ligation number reported to date for the ethynide moiety by adopting an unprecedented µ5 -η1 mode.

Supramolecular Structural Chemistry (a)

(b)

(c)

795 (d)

Fig. 20.4.34.

(a) Broken silver(I) double chain in 2[Ag2 (pC≡CC6 H4 C≡C)]·11AgCF3 CO2 · 4CH3 CN·2CH3 CH2 CN stabilized by continuous π –π stacking between parallel p-phenylene rings. (b) Silver double chain in Ag2 (m-C≡CC6 H4 C≡C)·6AgCF3 CO2 ·3CH3 CN·2.5H2 O assembled by argentophilic interaction and π–π interaction between adjacent pairs of m-phenylene rings. (c) Widened silver chain in 3[Ag2 (o-C≡CC6 H4 C≡C)]·14AgCF3 CO2 ·2CH3 CN·9H2 O constructed through the cross-linkage of two narrow silver chains by bridging silver atoms with pairwise π –π interaction between the o-phenylene rings. (d) Broken silver(I) double chain in Ag2 (m-C≡CC6 H4 C≡C)]·5AgNO3 ·3H2 O stabilized by continuous π −π stacking between parallel m-phenylene rings. From L. Zhao and T. C. W. Mak, J. Am. Chem. Soc. 127, 14966–7 (2005).

The Ag14 aggregate, being constructed essentially from two independent Agn ⊂C2 −(p-C6 H4 )−C2 ⊃Agn (n = 4, 5) synthons through argentophilic interaction and continuous π–π stacking, is connected to its symmetry equivalents to form a broken silver(I) double chain along the a-axis. Adjacent Ag14 segments within a single chain are bridged by the oxygen atoms of two independent trifluoroacetate groups, and the pair of single chains are arranged in interdigitated fashion [Fig. 20.4.34(a)]. In contrast to the popular µ1 ,µ1 -coordination mode of m-phenylenediethynide in most transition-metal complexes, this ligand exhibits two different terminal ethynide bonding modes, namely, µ4 -η1 ,η1 ,η1 ,η1 and µ4 -η1 ,η1 ,η1 ,η2 , in the crystal structure of Ag2 (m-C≡CC6 H4 C≡C)·6AgCF3 CO2 ·3CH3 CN·2.5H2 O. Through inversion centers located between successive pairs of m-phenylene rings, the Agn ⊂C2 −(m-C6 H4 )−C2 ⊃Agn (n = 4) synthon is extended along the a direction by Ag· · · Ag interactions to form a silver double chain [Fig. 20.4.34(b)], which are further consolidated by π − π interaction between adjacent m-phenylene rings protruding alternatively on either side. In the crystal structure of 3[Ag2 (o-C≡CC6 H4 C≡C)]·14AgCF3 CO2 ·2CH3 CN·9H2 O, the ethynide moieties bond to silver atoms via three different coordination modes: µ4 -η1 ,η1 ,η1 ,η2 , µ4 -η1 ,η1 ,η2 ,η2 , and µ5 -η1 ,η1 ,η1 ,η1 ,η2 [Fig. 20.4.34(c)]. The two independent Agn ⊂ C2 −(o-C6 H4 )−C2⊃Agn (n = 4, 5) synthons mutually associate to generate an undulating silver chain consolidated by argentophilic interaction, pairwise π–π interaction between the o-phenylene rings, and linkage by silver atoms Ag3 and Ag9 across two silver single chains. Bridged by silver atom Ag10 through Ag· · · Ag interaction and three oxygen atoms (O2W, O4, O8), the silver columns are linked to form a wave-like layer with o-phenylene groups protruding on both sides.

796

Structural Chemistry of Selected Elements Carbon-chain

Fig. 20.4.35.

elongation

-----

Schematic diagram showing the structural relationship between the supramolecular synthons Ag4 ⊂C2 —C2 ⊃Ag4 , Agn ⊂ C2 —R—C2 ⊃Agn (R = p-, m-, o-C6 H4 ; n = 4, 5), and C2 @Agn (n = 6–10). The circular arc represents a Agn (n = 4, 5) basket.

Conceptual contraction

Variation of relative orientation of ethynide groups

The decreasing separation of the pair of ethynide groups in the above three complexes is accompanied by strengthened argentophilic interaction at the expense of weakened π–π stacking, yielding a broken double chain, a double chain and a silver layer, respectively. When the pair of ethynide vectors make an angle of 60◦ , sharing of a common silver atom for the Agn caps occurs in the o-phenylenediethynide complex. The crystal structure of Ag2 (m-C≡CC6 H4 C≡C)]·5AgNO3 ·3H2 O features a broken silver(I) double chain analogous to that of the p-phenylenediethynide complex [see Fig. 20.4.34(a). However, the single chains containing the Ag14 aggregates are arranged in parallel fashion, each matching Ag14 pair being connected by two m-phenylenediethynide ligands [Fig. 20.4.34(d)]. Linkage of a series of Agn ⊂C2 −(m-C6 H4 )−C2 ⊃Agn (n = 4) fragments by intrachain bridging nitrate groups with continuous π–π interaction between adjacent mphenylene rings engenders the broken silver(I) double chain. The structural correlation between various silver–ethynide supramolecular synthons affords a rationale for the preponderant existence of C2 @Agn (n = 6−10) polyhedra inAg2 C2 complexes (see Section 20.4.5). If the linear − C≡C– C≡C− chain were contracted to a C2− 2 dumbbell, further overlap between atoms of the terminal Agn caps would conceivably yield a closed cage with 6–10 vertices (Fig. 20.4.35). Silver(I) arylethynide complexes containing R-C2 ⊃ Agn (R = C6 H5 , C6 H4 Me-4, C6 H4 Me-3, C6 H4 Me-2, C6 Ht4 Bu-4; n = 4, 5) π–π Stacking or π–π interactions are important noncovalent intermolecular interactions, which contribute much to self-assembly when extended structures are formed from building blocks with aromatic moieties. In relation to the rich variety of π–π stacking in the crystal structure of silver(I) complexes of phenylenediethynide, related silver complexes of phenylethynide and its homologues with different substituents (–CH3 , –C(CH3 )3 ) or the –CH3 group in different positions (o-, m-, p-) are investigated. In the crystal structure of 2AgC≡CC6 H5 ·6AgC2 F5 CO2 ·5CH3 CN, the ethynide group composed of C1 and C2 is capped by a square-pyramidal Ag5 basket in an unprecedented µ5 -η1 ,η1 ,η1 ,η1 ,η2 coordination mode and the other one comprising C9 and C10 by a butterfly-shaped Ag4 basket in a µ4 η1 ,η1 ,η1 ,η2 coordination mode, as shown in Fig. 20.4.36(a). With an inversion center located at the center of the Ag1· · · Ag1A bond, two Ag5 baskets share an edge to engender a Ag8 aggregate, whereas another Ag8 aggregate results from fusion of a pair of inversion-related Ag4 baskets. Two adjacent Ag8 agregates (3)

Supramolecular Structural Chemistry (a)

797

(b)

Fig. 20.4.36.

(a) Coordination modes of the independent phenylethynide ligands in 2AgC≡CC6 H5 ·6AgC2 F5 CO2 ·5CH3 CN. (b) Coordination mode of the C6 H5 C≡C− ligand in AgC≡CC6 H5 ·3AgCF3 CO2 ·CH3 CN. The silver column is connected by edge-sharing between adjacent square-pyramidal Ag5 aggregates, and continuous π –π stacking of phenyl rings occurs on one side of the column. From L. Zhao, W.-Y. Wong and T. C. W. Mak, Chem. Eur. J. 12, 4865–72 (2006).

are linked by two pentafluoropropionate groups via µ3 -O, O, , O, and µ2 -O, O, coordination modes, respectively, to generate an infinite column along the [111] direction. No π–π interaction is observed in this complex. An infinite array of parallel phenyl rings stabilized by π –π stacking (centerto-center distance 418.9 pm) occurs in the complex AgC≡CC6 H5 ·3AgCF3 CO2 ·CH3 CN [Fig. 20.4.36(b)]. The capping square-planar Ag5 baskets are fused through argentophilic interactions via edge-sharing to form an infinite coordination column along the [100] direction, with continuous π –π stacking of phenyl rings lying on the same side of the column. When substituents are introduced into the phenyl group, the π–π stacking between consecutive aromatic rings is affected by the size of the substituted groups and their positions. In the crystal structure of 2AgC≡CC6 H4 Me-4·6AgCF3 CO2 ·1.5CH3 CN [Fig. 20.4.37(a)], the methyl group has a little influence on the formation of a silver column stabilized by π –π stacking, which is almost totally identical with the structure of AgC≡CC6 H5 ·3AgCF3 CO2 ·CH3 CN [see Fig. 20.4.36(b)]. However, when a more bulky tert-butyl group is employed, the π–π stacking system is interrupted despite the formation of a similar silver chain [Fig. 20.4.37(b)]. The entire C6 Ht4 Bu-4 moiety rotates around the C(t Bu)–C(phenyl) single bond to generate a highly disordered structure. On the other hand, putting a meta-methyl group on the phenyl ring can form C−H· · · π interaction, but the constitution of the silver chain is changed from edge-sharing to vertex-sharing [Fig. 20.4.37(c)]. Finally, use of the 2-methyl-substituted phenyl ligand entirely destroys the π–π stacking and even breaks the Ag· · · Ag interactions between Agn caps to form a silver chain connected by trifluoroacetate groups [Fig. 20.4.37(d)]. 20.4.7

Self-assembly of nanocapsules with pyrogallol[4]arene macrocycles

Recent studies have shown that the bowl-shaped C-alkyl substituted pyrogallol[4]arene macrocycles readily self-assemble to form a gobular hexameric cage, which is structurally robust and remains stable even in aqueous media (Fig. 20.4.38). Slow evaporation of a solution of C-heptylpyrogallol[4]arene in ethyl acetate gives crystalline [(C-heptylpyrogallol[4]arene)6 (EtOAc)6

798

Structural Chemistry of Selected Elements

(a)

(b)

(c)

(d)

Fig. 20.4.37.

(a) Silver column in 2AgC≡CC6 H4 Me-4 ·6AgCF3 CO2 ·1.5CH3 CN connected by the fusion of square-pyramidal Ag5 baskets and stabilized by continuous π–π stacking of phenyl rings. (b) Similar silver column in AgC≡CC6 Ht4 Bu-4·3AgCF3 CO2 ·CH3 CN connected only by argentophilic interaction. (c) Silver chain in AgC≡CC6 H4 Me-3·2AgCF3 SO3 through atom sharing. (d) Silver chain in AgC≡CC6 H4 Me-2·4AgCF3 CO2 ·H2 O through the connection of trifluoroacetate groups.

(H2 O)]·6EtOAc, and X-ray analysis revealed that the large spheroidal supermolecule is stabilized by a total of 72 O–H· · · O hydrogen bonds (four intramolecular and eight intermolecular per macrocycle building block). The nano-sized molecular capsule, having an internal cavity volume of about 1.2 nm3 , contains six ethyl acetate molecules and one water molecule; the methyl terminal of each encapsulated ethyl acetate guest molecule is orientated toward a bulge on the surface, and the single guest water molecule resides at the center of the capsule. In the crystal structure, the external ethyl acetate solvate molecules are embedded within the lower rim alkyl legs at the base of each of the macrocycles, and the nanocapsules are arranged in hexagonal closest packing. HO

OH

HO

R

HO

R

R

OH

R

OH

R = C7H15

HO

R

R

R

R

R

R HO

R

OH

R HO

R

OH

R R

R

R

R

R

OH

R

R

R

R

R

Fig. 20.4.38.

Assembly of six C-heptylpyrogallol[4]arene molecules by intra- and intermolecular hydrogen bonds to form a globular supermolecule with a host cavity of volume ∼ 1.2 nm3 . H atoms are omitted for clarity, and hydrogen bonds are represented by dotted lines. From G. V. C. Cave, J. Antesberger, L. J. Barbour, R. M. McKinley and J. L. Atwood, Angew. Chem. Int. Ed. 43, 5263-6 (2004).

With reference to the unique architecture of this hydrogen-bonded hexameric capsule I [Fig. 20.4.39(a)], it was noted that the pyrogallol[4]arene building block has the potential of serving as a multidentate ligand through deprotonation of some of the upper rim phenolic groups. As envisaged, treatment of

Supramolecular Structural Chemistry (a)

799

(b) Fig. 20.4.39.

capsule I

capsule II

C-propan-3-ol pyrogallol[4]arene with four equivalents of Cu(NO3 )2 ·3H2 O in a mixture of acetone and water yielded a large neutral coordination capsule II [Cu24 (H2 O)x (C40 H40 O16 )6 (acetone)n ] where x ≥ 24 and n = 1–6. Singlecrystal X-ray analysis established that retro-insertion of 24 Cu(II) metal centers into the hexameric framework results in substitution of 48 of the 72 phenolic protons, leaving the remaining 24 intact for intramolecular hydrogen bonding (O· · · O 0.2400–0.2488 nm). As shown in Fig. 20.4.39(b), the large coordination capsule II may be viewed as an octahedron with the six 16-membered macrocylic rings located at its corners, and each of its eight faces is capped by a planar cyclic [Cu3 O3 ] unit of dimensions Cu–O 0.1911 to 0.1980 nm, O–Cu–O 85.67◦ to 98.23◦ , and Cu–O–Cu 140.96◦ to 144.78◦ . Definitive location of all guest molecules inside the cavity is somewhat ambiguous owing to inexact stoichiometry and disorder. However, the (+)MALDI mass spectra of II indicate that each individual capsule encloses different mixtures of water and acetone. In particular, two peaks implicated the presence of 24 entrapped water molecules that occupy axial coordination sites orientated toward the center of the cavity. The pair of supramolecular capsules I and II represents a landmark in the construction of large coordination cages using multicomponent ligands. This elegant blueprint approach is facilitated by the robustness of the hydrogenbonded assembly I, which serves as a template for metal-ion insertion at specific sites with conservation of structural integrity. Notably, capsule size is virtually unchanged as the center-to-corner distance of the four phenolic O atoms belonging to the eight-membered intermolecular hydrogen-bonded ring (0.1883–0.1976 nm) in I closely matches the Cu–O bond distance of 0.1913–0.1978 nm in II.

20.4.8

Reticular design and synthesis of porous metal–organic frameworks

The design and synthesis of metal–organic frameworks (MOFs) has yielded a large number of solids that possess useful gas and liquid adsorption properties. In particular, highly porous structures constructures constructed from discrete

Hydrogen-bonded supramolecular capsule I compared with coordination capsule II. The external aliphatic groups are omitted for clarity. Note that a pair of intermolecular O–H· · · O hydrogen bonds is replaced by four square-planar Cu–O coordination bonds in the metal-ion insertion process that generates the isostructural inorganic analog. From R. M. McKinley, G. V. C. Cave and J. L. Atwood, Proc. Nat. Acad. Sci. 102, 5944-8 (2005).

800

Structural Chemistry of Selected Elements (a)

(b)

Fig. 20.4.40.

Crystal structure of MOF-5. (a) Zn4 O tetrahedra joined by benzenedicarboxylate linkers. H atoms are omitted for clarity. (b) The topology of the framework (primitive cubic net) shown as an assembly of (Zn4 O)O12 clusters (represented as truncated tetrahedra) and p-phenylene (–C6 H4 –) links (represented by rods). From O. M. Yaghi, M. O’Keeffe, N. W. Ockwig, H. K. Chae, M. Eddaoudi, and J. Kim, Nature 423, 705-14 (2003).

metal–carboxylate clusters and organic links have been demonstrated to be amenable to systematic variation in pore size and functionality. Consider the structure of the discrete tetranuclear Zn4 O(CH3 CO2 )6 molecule, which is isostructural with Be4 O(CH3 CO2 )6 , the structure of which is shown in Fig. 9.5.2. Replacement of each acetate ligand by one half of a linear dicarboxylate produces a molecular entity that can conceivably be interconnected to identical entities to generate an infinite coordination network. An illustrative example is Zn4 O(BDC)6 , referred to as MOF-5, which is prepared from Zn(II) and benzene-1,4-dicarboxylic acid (H2 BDC) under solvothermal conditions. In the crystal structure, a Zn4 O(CO2 )6 fragment comprising four fused ZnO4 tetrahedra sharing a common vertex and six carboxylate C atoms constitute a “secondary building unit” (SBU). Connection of such octahedral SBUs by mutually perpendicular p-phenylene (−C6 H4 −) links leads to an infinite primitive cubic network, as shown in Fig. 20.4.40. Alternatively, the smaller Zn4 O fragment (an oxo-centered Zn4 tetrahedron) can be regarded as the SBU and the corresponding organic linker is the whole benzene-1,4-dicarboxylate dianion. The resulting MOF-5 structure has exceptional stability and porosity as both the SBU and organic link are relatively large and inherently rigid. This reticular [which means ‘having the form of a (usually periodic) net] design strategy, based on the concept of discrete SBUs of different shapes (triangles, squares, tetrahedra, octahedra, etc.) considered as “joints” and organic links considered as “struts”, has been applied to the synthesis and utilization of a vast number of MOF structures exhibiting varying geometries and network topologies. Based on the Zn4 O(CO2 )6 SBU in the prototype MOF-5 (also designated as IRMOF1), a family of isoreticular and isostructural cubic frameworks with diverse pore sizes and functionalities has been constructed, including IRMOF-6, IRMOF-8, IRMOF-11, and IRMOF-16, which are illustrated in Fig. 20.4.41. An example of a porous framework that is isoreticular, but not isostructural, with MOF-5 is MOF-177, which incorporates the extended organic linker 1,3,5-benzenetribenzoate (BTB). The framework of crystalline MOF177, Zn4 O(BTB)2 · (DEF)15 (H2 O)3 , where DEF = diethyl formamide, has an ordered structure with an estimated surface area of 4,500 m2 g−1 , which greatly exceeds those of zeolite Y (904 m2 g−1 ) and carbon (2,030 m2 g−1 ).

Supramolecular Structural Chemistry

801

IRMOF-1 (≡ MOF-5)

IRMOF-11

IRMOF-6

Fig. 20.4.41.

IRMOF-16

IRMOF-8

As shown in Fig. 20.4.42, the underlying topology of MOF-177 is a (6,3)net with the center of the octahedral Zn4 O(CO2 )6 cluster as the six-connected node and the center of the BTB unit as the three-connected node. Its exceptionally large pores are capable of accommodating polycyclic organic guest molecules such as bromobenzene, 1-bromonaphthalene, 2-bromonaphthalene, 9-bromoanthracene, C60, and the polycyclic dyes Astrazon Orange R and Nile Red. Furthermore, the ability to prepare these kinds of MOFs in high yield and with adjustable pore size, shape, and functionality has led to their exploration as gas storage materials. Thermal gravimetric and gas sorption experiments have shown that IRMOF-6, bearing a fused hydrophobic unit C2 H4 in its organic link, has the optimal pore aperture and rigidity requisite for maximum uptake of methane. Activation of the porous framework was achieved by exchanging the included guest molecules with chloroform, which was then removed by

Comparison of cubic fragments in the respective three-dimensional extended structures of IRMOF-1 (≡ MOF-5), IRMOF-6, IRMOF-8, IRMOF-11, and IRMOF-16. From M. Eddaoudi, J. Kim, N. Rosi, D. Vodak, J. Wachter, M. O’Keeffe and O. M. Yaghi, Science 295, 469-72 (2004).

802

Structural Chemistry of Selected Elements (a)

(b)

Fig. 20.4.42.

Crystal structure of MOF-177. (a) A central Zn4 O unit coordinated by six BTB ligands. (b) The structure viewed down [001]. From H. K. Chae, D. Y. Siberio-Pérez, J. Kim, Y. B. Go, M. Eddaoudi, A. J. Matzger, M. O’Keeffe and O. M. Yaghi, Nature 427, 523-7 (2004).

gradual heating to 800◦ C under an inert atmosphere. The evacuated framework has a stability range of 100-400◦ C, and the methane sorption isotherm measured in the range 0-40 atm at room temperature has an uptake of 240 cm3 (STP)/g [155 cm3 (STP)/cm3 ] at 298 K and 36 atm. On a volume-to-volume basis, the amount of methane sorbed by IRMOF-6 at 36 atm amounts to 70% of that stored in compressed methane cylinders at ∼205 atm. As compared to IRMOF6, IRMOF-1 under the same conditions has a smaller methane uptake of 135 cm3 (STP)/g. The isoreticular MOFs based on the Zn4 O(CO2 )6 SBU also possesses favorable sorption properties for the storage of molecular hydrogen. At 77 K, microgravimetric sorption measurements gave H2 (mg/g) values of 13.2, 15.0, 16.0, and 12.5 for IRMOF-1, IRMOF-8, IRMOF-11, and MOF-177, respectively. At the highest pressures attained in the measurements, the maximum uptake values for these frameworks are 5.0, 6.9, 9.3, and 7.1 molecules of H2 per Zn4 OLx unit where L stands for a linear dicarboxylate. MOF-177 has been demonstrated to act like a super sponge in capturing vast quantities of carbon dioxide at room temperature. At moderate pressure (about 35 bar), its voluminous pores result in a gravimetric CO2 uptake capacity of 33.5 mmol/g, which far exceeds those of the benchmark adsorbents zeolite 13X (7.4 mmol/g at 32 bar) and activated carbon MAXSORB (25 mmol/g at 35 bar). In terms of volume capacity, a container filled with MOF-177 can hold about twice the amount of CO2 versus the benchmark materials, and 9 times the amount of CO2 stored in an empty container under the same conditions of temperature and pressure. The previous structural and sorption studies of MOFs are all based on the discrete Zn4 O(CO2 )6 SBU. Recent development has demonstrated that rod-shaped metal–carboxylate SBUs can also give rise to a variety of stable solid-state architectures and permanent porosity. Three illustrative examples are presented below. In the crystal structure of Zn3 (OH)2 (BPDC)2 ·(DEF)4 (H2 O)2 where BPDC = 4,4’-biphenyldicarboxylate (MOF-69A), there are tetrahedral and octahedral Zn(II) centers coordinated by four and two carboxylate groups, respectively,

Supramolecular Structural Chemistry

803

in the syn,syn mode, with each µ3 -hydroxide ion bridging three metal centers [Fig. 20.4.43(a)]. The infinite Zn–O–C rods are aligned in parallel fashion and laterally connected to give a three-dimensional network [Fig. 20.4.43(b)], forming rhombic channels of edge 1.22 nm and 1.66 nm along the longer diagonal, into which the DMF and water guest molecules are fitted. (a)

(b)

Fig. 20.4.43.

Channel structure of MOF-69A: (a) ball-and-stick representation of inorganic SBU; (b) SBUs connected by biphenyl links. The DEF and water molecules have been omitted for clarity. From N. L. Rosi, J. Kim, M. Eddaoudi, B. Chen, M. O’Keeffe and O. M. Yaghi, J. Am. Chem. Soc. 127, 1504–18 (2005).

The Mn–O–C rods in MOF-73, Mn3 (BDC)3 ·(DEF)2 , are constructed from a pair of linked six-coordinate Mn(II) centers [Fig. 20.4.44(a)]. One metal center is bound by two carboxylate groups acting in the syn,syn mode, one in the bidentate chelating mode, and a fourth one in the syn,anti mode. The other metal center has four carboxylates bound in the syn,syn mode and two in the syn,anti mode. Each rod is built of corner-linked and edge-linked (a)

(b)

Fig. 20.4.44.

Channel structure of MOF-73: (a) ball-and-stick representation of inorganic SBU; (b) SBUs connected by p-phenylene links. The DEF molecules have been omitted for clarity. From N. L. Rosi, J. Kim, M. Eddaoudi, B. Chen, M. O’Keeffe and O. M. Yaghi, J. Am. Chem. Soc. 127, 1504–18 (2005).

804

Structural Chemistry of Selected Elements MnO6 octahedra, and is connected to four neighboring rods by p-phenylene links. The resulting three-dimensional host framework [Fig. 20.4.44(b)] has rhombic channels of dimensions 1.12 × 0.59 nm filled by the DEF guest molecules. The structure of MOF-75, Tb(TDC)·(NO3 )(DMF)2 where TDC = 2,5thiophenedicarboxylate, contains eight-coordinate Tb(III) bound by four carboxylate groups all acting in the syn,syn mode, one bidentate nitrate ligand, and two terminal DMF ligands [Fig. 20.4.45(a)]. The Tb–O–C rod orientated in the a direction consists of linked TbO8 bisdisphenoids with the carboxyl carbon atoms forming a twisted ladder. Lateral linkage of rods in the b and c directions by the thiophene units generate rhombic channels measuring 0.97 × 0.67 nm, as illustrated in Fig. 20.4.45(b), which accommodate the DMF guest molecules and nitrate ions. 20.4.9

One-pot synthesis of nanocontainer molecule

Dynamic covalent chemistry has been used in an atom-efficient self-assembly process to achieve a nearly quantitative one-pot synthesis of a nanoscale molecular container with an inner cavity of approximately 1.7 nm3 . In a thermodynamically driven, trifluoroacetic acid catalyzed reaction in chloroform, six cavitands 1 and twelve ethylenediamine linkers condense to generate an octahedral nanocontainer 2, as shown in Fig. 20.4.46. Each cavitand has 4 formyl groups on its rim, and these react with the 24 amino groups of the linkers to form 24 imine bonds. After reduction of all the imine bonds with NaBH4 , the hexameric nanocontainer can be isolated via reversed-phase HPLC as the trifluoroacetate salt 2·24CF3 COOH in 63% yield based on 1. Elemental analysis of the white solid corresponds to the stoichiometric formula 2·24CF3 COOH·9H2 O. The simplified 1 H and 13 C NMR spectra of 2 and 2·24CF3 COOH are consistent with their octahedral symmetry. If the same reaction is carried out with either 1,3-diaminopropane or 1,4diaminobutane in place of ethylenediamine, the product is an octaimino hemicarcerand composed of two face-to-face cavitands connected by four diamino bridging units. 20.4.10

Filled carbon nanotubes

Much research has been devoted to the insertion of different kinds of crystalline and non crystalline material into the hollow interior of carbon nanotubes. The encapsulated species include fullerenes, clusters, one-dimensional (1D) metal nanowires, binary metal halides, metal oxides, and organic molecules. The left side of Fig. 20.4.47 illustrates the van der Waals surfaces of the (10,10) and (12,12) armchair SWNTs with diameters of 1.36 and 1.63 nm and corresponding internal diameters of approximately 1.0 and 1.3 nm, respectively, as specified by the van der Waals radii of the sp2 carbon atoms forming the walls. The (10,10) tube has the right size to accommodate a linear array of C60 molecules, as shown by the HRTEM images marked (a) and (b) on the right side of Fig. 20.4.47. Parts (c) and (d) show the HRTEM image and modeling of an interface between four fullerene molecules and a 1D FeI2 crystal.

Supramolecular Structural Chemistry

(a)

805

(b)

Fig. 20.4.45.

Channel structure of MOF-75: (a) ball-and-stick representation of inorganic SBU; (b) SBUs connected by thiophene links. The DMF molecules and nitrate ions have been omitted for clarity. From N. L. Rosi, J. Kim, M. Eddaoudi, B. Chen, M. O’Keeffe and O. M. Yaghi, J. Am. Chem. Soc. 127, 1504–18 (2005).

H

O

H C5H11

O H

O

O

O

O H

O

H

H

O O

H

H O

O

O

O

O

H C5H11

C5H11

O

H

O O

≡

H C5H11

H

O H

O

H O

H

1

CF3CO2H cat. H

6

CHCl3, 22 οC

+ 12 en

N

− 24H2O H

2

+ H2N CH2

CH2 H2N+ CF3CO2−

C

C

H

N

1. NaBH4 2. HCl/MeOH 3. HPLC (MeOH/H2O/TFA)

CF3CO2−

2 · 24CF3COOH Fig. 20.4.46.

Reaction scheme showing the thermodynamically controlled condensation of tetraformylcavitand 1 with ethylenediamine to form an octahedral nanocontainer 2, which undergoes reduction to yield the trifluoroacetate salt 2·24CF3 COOH.

806

Structural Chemistry of Selected Elements (a) (10,10)

(12,12)

(b)

0.17nm

~1.36nm

~1.2nm

0.17nm (c)

~1.45nm

1.63nm

(d)

Fig. 20.4.47.

Left: Schematic representations of the van der Waals surfaces of (10,10) and (12,12) armchair SWNTs. Right: (a) HRTEM image showing a (10,10) SWNT filled with C60 molecules. (b) Second image from the same specimen as in (a), showing a cross-sectional view of an ordered bundle of SWNTs, some of which are filled with fullerene molecules. (c) HRTEM image (scale bar = 1.5 nm) of a filled SWNT showing an interface between four C60 molecules (a possible fifth molecule is obscured at the left) and a 1D FeI2 crystal. (d) Schematic structural representation of (c) (Fe atoms = small spheres; I atoms = large spheres). Courtesy of Professor M. L. H. Green.

The formation of an ordered 2 × 2 KI crystal column within a (10,10) SWNT with D ∼ 1.4 nm is shown in Fig. 20.4.48. The structural model is illustrated in (a), and a cross-sectional view is shown in (b). The coordination numbers of the cation and anion are changed from 6:6 in bulk KI to 4:4 in the 2 × 2 column. Each dark spot in the HRTEM image (c) represents an overlapping I–K or K–I arrangement viewed in projection, which matches the simulated image (d). The spacing between spots along the SWNT is ∼0.35 nm, corresponding to the {200} spacing in bulk KI, whereas across the SWNT capillary the spacing increases to ∼0.4 nm, representing a ∼17% tetragonal expansion. The incorporation of a 3 × 3 KI crystal in a wider SWNT (D ∼ 1.6 nm) is depicted in Fig. 20.4.49. In this case, three different coordination types (6:6, 5:5, and 4:4) are exhibited by atoms forming the central, face, and corner · · · I– K–I–K· · · rows of the 3 × 3 column, respectively, along the tube axis. The projection shows the K+ and I− sublattices as pure element columns,

Supramolecular Structural Chemistry

(a)

807

0.35nm

:C

:I

:K

1.36nm

0.4nm

Fig. 20.4.48.

(c)

A 2 × 2 KI crystal column filling a (10,10) SWNT. (a) Cutaway structural representation of composite model used in the simulation calculations. (b) End-on view of the model, showing an increased lattice spacing of 0.4 nm across the capillary in two directions (assuming a symmetrical distortion). (c) HRTEM image. (d) Simulated Image. Courtesy of Professor M. L. H. Green.

(b)

0.275nm

(a)

0.246nm

(d)

0.4nm

0.275nm 0.246nm

(b)

0.695 nm 2

–



0.3 nm

–

1.6nm Fig. 20.4.49.

(a) Reconstructed HRTEM image (averaged along the tube axis) of the projection of a 3 × 3 KI crystal in a D ∼1.6 nm diameter SWNT. Note that the contrast in this image is reversed so that regions of high electron density appear bright and low electron density appear dark. (b) Structural model derived from (a). Courtesy of Professor M. L. H. Green.

808 Fig. 20.4.50.

(a) An isolated DWNT filled with KI. (b) Reconstructed image of the KI@DWNT composite; the marked area was structurally analyzed in detail. (c) Crystal model showing the distortions imposed and the three subsections considered for its construction. (d) Structural model of the marked section in (b). (e) Reconstructed versus simulated image of the three sections. Courtesy of Professor M. L. H. Green.

Structural Chemistry of Selected Elements (a)

(b) 2 nm

(c) I

II

III

(e)

5

I

(d)

II

3 7 7 7

III

5 nm

2 nm

which are distinguishable by their scattering powers. The iodine atoms located along all show a slight inward displacement relative to their positions in bulk KI, whereas the K atoms located along the same cell diagonal exhibit a small expansion. It was found that KI can also be used to fill a DWNT, as shown in Fig. 20.4.50. The HRTEM image (a) and reconstructed image (b) of the KIDWNT composite was analysed using a model composed of an inner (11, 22) SWNT (D ∼ 2.23 nm) and an outer (18, 26) SWNT (D ∼ 3.04 nm). The measured averaged spacings between the atomic columns gave values of 0.37 nm across the DWNT axis and 0.36 nm along it, which agree well with the {200} d-spacing of rock-salt KI (0.352 nm). In the simulation calculation, the encapsulated fragment was divided into three sections in order to model the lattice defects such as plane shear and plane rotation.

References 1. G. A. Jeffrey, An Introduction to Hydrogen Bonding, Oxford University Press, New York, 1997. 2. G. R. Desiraju and T. Steiner, The Weak Hydrogen Bond in Structural Chemistry and Biology, Oxford University Press, New York, 1999. 3. J.-M. Lehn, Supramolecular Chemistry: Concepts and Perspectives, VCH, Weinheim, 1995. 4. P. J. Cragg, A Practical Guide to Supramolecular Chemistry, Wiley, Chichester, 2005. 5. J. W. Steed, D. R. Turner and K. J. Wallice, Core Concepts in Supramolecular Chemistry and Nanochemistry, Wiley, Chichester, 2007. 6. J. W. Sneed and J. L. Atwood, Supramolecular Chemistry, Wiley, Chichester, 2000. 7. K. Ariga and T. Kunitake, Supramolecular Chemistry—Fundamentals and Applications, Springer-Verlag, Heidelberg, 2006. 8. G. R. Desiraju (ed.), The Crystal as a Supramolecular Entity, Wiley, Chichester, 1996. 9. G. R. Desiraju (ed.), Crystal Design: Structure and Function, Wiley, Chichester, 2003. 10. A. Bianchi, K. Bowman-James and E. Garcia-España (eds.), Supramolecular Chemistry of Anions, Wiley–VCH, New York, 1997. 11. J.-P. Sauvage (ed.), Transition Metals in Supramolecular Chemistry, Wiley, Chichester, 1999.

Supramolecular Structural Chemistry 12. M. Fujita (ed.), Molecular Self-assembly: Organic versus Inorganic Approaches (Structure and Bonding, vol. 96), Springer, Berlin, 2000. 13. F. Toda and R. Bishop (eds.), Separations and Reactions in Organic Supramoilecular Chemistry, Wiley, Chichester, 2004. 14. N. Yui (ed.), Supramolecular Design for Biological Applications, CRC Press, Boca Raton, FL, 2003. 15. I. Haiduc and F. T. Edelmann (eds.), Supramolecular Organometallic Chemistry, Wiley–VCH, Weinheim, 1999. 16. W. Jones and C. N. R. Rao (eds.), Supramolecular Organization and Materials Design, Cambridge University Press, Cambridge, 2002. 17. D. Wöhrle and A. D. Pomogailo, Metal Complexes and Metals in Macromolecules, Wiley–VCH, Weinheim, 2003. 18. E. R. T. Tiekink and J. J. Vittal (eds.), Frontiers in Crystal Engineering, Wiley, Chichester, 2006. 19. J. L. Atwood and J. W. Steed (eds.), Encyclopedia of Supramolecular Chemistry, Marcel-Dekker, New York, 2004. 20. D. N. Chin, J. A. Zerkowski, J. C. MacDonald and G. M. Whitesides, Strategies for the design and assembly of hydrogen-bonded aggregates in the solid state, in J. K. Whitesell (ed.), Organised Molecular Assemblies in the Solid State, Wiley, Chichester, 1999. 21. G. A. Ozin and A. C. Arsenault, Nanochemistry: A Chemistry Approach to Nanomaterials, RSC Publishing, Cambridge, 2005. 22. Q. Li and T. C. W. Mak, Novel inclusion compounds with urea/thiourea/selenoureaanion host lattices, in M. Hargittai and I. Hargittai (eds.), Advances in Molecular Structure Research, vol. 4, pp. 151–225, Stamford, Connecticut, 1998. 23. M. I. Bruce and P. J. Low, Transition metal complexes containing all-carbon ligands. Adv. Organomet. Chem. 50, 179–444 (2004). 24. V. W. W. Yam and E. C. C. Cheng, Silver organometallics, in D. M. P. Mingos and R. H. Crabtree (eds.), Comprehensive Organometallic Chemistry III, vol. 2 (K. Meyer, ed.), pp. 197–249, Elsevier, Oxford, 2007. 25. T. C. W. Mak, X.-L. Zhao, Q.-M. Wang and G.-C. Guo, Synthesis and structural characterization of silver(I) double and multiple salts containing the acetylenediide dianion. Coord. Chem. Rev. 251, 2311–33 (2007). 26. L. Zhao and T.C.W. Mak, Multinuclear silver-ethynide supramolecular synthons for the construction of coordination networks. Chem. Asian J. 2, 456–467 (2007). 27. L. Zhao, X.-L. Zhao and T. C. W. Mak, Assembly of infinite silver(I) columns, chains, and bridged aggregates with supramolecular synthon bearing substituted phenylethynides, Chem. Eur. J. 13, 5927–36 (2007). 28. J. Lagona, P. Mukhopadhyay, S. Charkrabarti and L. Issacs, The cucurbit[n]uril family. Angew. Chem. Int. Ed. 44, 4844–70 (2005). 29. N. W. Ockwig, O. Delgardo-Friedrichs, M. O’Keeffe and O. M. Yaghi, Reticular chemistry: occurrence and taxonomy of nets and grammar for the design of frameworks. Acc. Chem. Res. 38, 176–82 (2005). 30. X. Liu, Y. Liu, G. Li and R. Warmuth, One-pot, 18-component synthesis of an octahedral nanocontainer molecule. Angew. Chem. Int. Ed. 45, 901–4 (2006). 31. J. Sloan, A. I. Kirkland, J. L. Hutchison and M. L. H. Green, Integral atomic layer architectures of 1D crystals inserted into single walled carbon nanotubes. Chem. Commun., 1319–32 (2002). 32. J. Sloan, A. I. Kirkland, J. L. Hutchison and M. L.H. Green, Aspects of crystal growth within carbon nanotubes. C. R. Physique 4, 1063–74 (2003).

809

810

Structural Chemistry of Selected Elements 33. P. M. F. J. Costa, S. Friedrichs, J. Sloan and M. L. H. Green, Imaging lattice defects and distortions in alkali-metal iodides encapsulated within double-walled carbon nanotubes. Chem. Mater. 17, 3122–9 (2005). 34. P. M. F. J. Costa, J. Sloan and M. L. H. Green, Structural studies on single- and double-walled carbon nanotubes filled with ionic and covalent compounds. Ciencia e Tecnologia dos Materiais 18, no. 3–4, 78–82 (2006).

Index ab initio methods, 142 acentric crystal classes, 304 acetylenediide, 530 acetylenediide, alkaline-earth, 530 acetylenediide, copper(I) complex, 532 acetylenediide, ternary metal, 530 acetylenide, 530 acid hydrates, 626 active space, 146 adamantane, disordered cubic form, 357, 361 adamantane, ordered tetragonal form, 358, 361 adamantane-1,3,5,7-tetracarboxylic acid, 741 adamantane-like cage compounds, 358, 362 adamantane-like molecular skeleton, 174 agostic bond, 402, 425 agostic-bond complexes, 428 alkali metal complexes, 436 alkali metal oxides, 433 alkali metal suboxides, 433 alkalides, 447 alkaline-earth metallocenes, 455 alkaline-earth oxides, 367 allophanate, 781 alnicos, 392 alums, MI MIII (XO4 )2 ·12H2 O, 353, 356 ammonia, 578 amorphous carbon, 506 angular correlation, 47 angular momentum quantum number, 31, 55 angular momentum, orbital, 55 angular momentum, spin, 55 angular momentum, total, 56 angular wavefunction, 30, 31, 33 anionic carbonyl cluster, 718 antibonding effect, 83 antibonding molecular orbital, 85, 89 argentophilic interaction, 785, 792, 795, 796, 797 argentophilicity (argentophilic attraction), 724 asymmetric molecule, 170 asymmetric unit, 319, 323 atomic orbital, 8 atomic orbitals, 31 atomic orbitals, energies of, 55 atomic units, 42 aurophilicity (or aurophilic attraction), 721 axial ratios, 301

azide ion, coordination modes, 562 azide ion, N− 3 , 562 azides, 562 band gap, 130 bands d–d, 271, 292 band theory, 128 barium titanate, BaTiO3 , 388 basic beryllium acetate, Be4 O(CH3 COO)6 , 336, 338 basis set, 142 benzene, supercrowded, 510 benzene-1,4-dicarboxylic acid, 800 benzenetribenzoate, 1,3,5-, 800 beryl, Be3Al2 [Si6 O18 ], 351, 353 betaine, 787 binaphthyl, 1,1, -, 345 binaphthyl, 1,1’-, 347 biphenyl, 333, 336, 337 bismuth-bismuth double bond, 606 bismuthine, tetrameric, 605 bismuthonium ylide, 604 body-centered cubic packing (bcp), 381 Bohr radius, 7, 34 boiling points of metallic elements, 133 Boltzmann weighting factor, 135 bond order, 94 bond valence, 703 bond valence of metal-metal bond, 711 bond-angle relationships for Td molecules, 175 bonding effect, 111 bonding molecular orbital, 84 boranes, 470 boranes, macropolyhedral, 479 boranes, metalla, 483 boranes, topological description, 471 boranes, arachno, 474 boranes, hypercloso, 483 boranes, hypho, 473, 475 boranes, closo, 477 boranes, nido, 474 borate, dihydrogen, 487 borates, structural principles, 489 borates, structural units, 487 borax, 489 borazine, 468 boric acid, 486

812

Index borides, metal, 464 borides, non-metal, 467 borides, rare-earth metal, 466 Born-Landé equation, 124 Born-Mayer equation, 124 boron carbides, 467 boron halides, 469 boron nitrides, 468 boron, α-R12, 461 boron, α-rhombohedral, 350, 352 boron, β-R105, 463 boron, β-R105 electronic structure, 481 boron, B12 icosahedron, 461 Borromean link, 753 Bravais lattices, 306, 309 butadiene, cyclization, 113 butadiene, equilibrium bond length, 113 butadiynediide, 792

cadmium iodide, CdI2 , 377 calcium carbide (Form I), CaC2 , 346, 348 calcium carbide, CaC2 , 369 calcium carbide, modifications, 530 calcium nitridoberyllate, Ca[Be2 N2 ], 346, 348 calix[4]arene bismelamine, 744 calomel, Hg2 Cl2 , 346, 348 carbide complex, terminal, 528 carbide-centered carbonyl clusters, 528 carbon atom, naked, 527 carbon black (soot), 506 carbon bridgehead, inverted bond configuration, 525 carbon fibers, 506 carbon nanotube, double-walled (DWNT), 807 carbon nanotube, filled, 804 carbon nanotube, multi-walled (MWNT), 508 carbon nanotube, single-walled (SWNT), 507, 804 carbon onions, 506 carbon, activated, 506 carbon, bond lengths, 520 carbon, coordination numbers, 520 carbon, covalent bond types, 517 carbon, hybridization schemes, 518 carbon-carbon bonds, abnormally long, 524 carbon-carbon single bonds, abnormally short, 526 carbonyl stretching modes in metal complexes, 246 carborane, actina, 485 carboranes, 470 carboranes, metalla, 483 carboxylic acid dimer synthon, 740 carcerand, 753 catenane, 753 cavitand, 804

centrifugal distortion constant, 159 cesium chloride, CsCl, 384 cesium iron fluoride, Cs3 Fe2 F9 , 352, 354 character tables, 180, 183 charge transfer transitions, 271 charge transfer, L → M, 291 charge transfer, M → L, 291 chelating β-diketiminate ligand, 494 cisplatin, 340, 342 clathrate hydrate, type I, 6GL ·2GS ·46H2 O, 361, 365 clathrate hydrate, type II, 8GL ·16GS ·136H2 O, 360, 363 clathrate hydrates, 625 cluster complexes, of Ge, Sn and Pb, 551 cluster compounds, 703 coal, 506 coke, 506 color center, 20 color center, or F-center, 368 complete basis set (CBS) methods, 151 complexes containing naked carbon atom, 527 composite methods, 151 concerted reactions, 113 condensed phase, 139 conduction band, 129 configuration energy, 67 configuration interaction (CI), 145 conglomerate, 338, 340 conrotatory process, 114 conservation of orbital symmetry, 113 coordinates of equipoints, 313, 317 coordination compounds of Group 2 elements, 451 coordination polymer, 757, 776 correlation energy, 145 corundum, α-Al2 O3 , 379 coulomb integral, 52 coupled cluster (CC) method, 146 coupled cluster singles and doubles (CCSD) method, 146 coupling, L–S, 56 coupling, j–j, 62 covalent radii, 99, 109 crinkled tape, 744 croconate, 783 crystal classes (crystallographic point groups), 301 crystal engineering, 737 crystal field theory (CFT), 261 crystal form, 300 crystal radii of ions, 121 crystal system, 307, 310 cubane, 349, 351 cubane-like molecular skeleton, 174 cubic closest packing (ccp), 364 cubic groups, 177

Index cubic molecular box, 763 cucurbituril, 772 cyanuric acid, 744 cyaphide, 599 cyclic conjugated polyenes, 221 cycloheptatrienyl ligand, 520 cyclopentadienyl complexes, of Ge, Sn and Pb, 549 de Broglie wavelength, 4 degenerate states, 19 degree of interpenetration, 769 degrees of freedom, 236 deltate, C3 O2− 3 , 524 density functional theory (DFT), 142 density of states function, 129 depolarization ratio, 238 depolarized vibrational band, 239 determinantal wavefunction, 48 Dewar benzene derivative, C18 H14 , 344, 346 diamond, cubic, 500 diamond, hexagonal, 500 diamondoid network, 768 diatomic molecules, 91 diazene (or diimide), 578 dibismuthene, 605 diethylbarbituric acid, 5,5-, 744 diffuse functions, 144 dihydrogen bond, X–H· · · H–E, 413 dihydrogen borate, 780 diiodides of Tm, Dy and Nd, 700 dinitrogen complex of samarium, 700 dinitrogen complexes, 564 dinitrogen, bonding to transition metals, 568 dinitrogen, oordination modes, 566 dinuclear complexes, 707 dioxygen carriers, 618 dioxygen metal complexes, 616 dioxygen species, 610 direct product, 185 disilene, 539 disilenes, 537 dispersion energy, 136 disrotatory process, 114 dissymmetric molecule, 171 disulfide, coordination modes, 632 dodecahedron, pentagonal, 177 dodecahedron, triangulated, 177 donor-acceptor complexes, of Ge, Sn and Pb, 554 double cage, 787 double group, 281 double zeta basis set, 143 dual nature of matter, 4 effective ionic radii, 122 effective nuclear charge, 54, 67

813 eigenfunction, 9 eigenvalue, 9 eighteen-electron rule, 288 electrical conductivity, 128 electrides, 447 electron affinity, 64, 66 electron cloud, 8 electron correlation, 47, 144 electronegativities, 133 electronegativity, 64, 67 electronic configuration, 48, 64 electronic configuration, equivalent, 60 electronic configuration, ground, 72 electronic spectra of some metal complexes, 274 electronic spectra of square planar complexes, 289 electronic transition, 53 electronic wavefunction, 6 electrostatic interaction, 135 enantiomorphous pairs, 314, 318 energy level diagram for octahedral complex, 268 energy level diagram for square planar complex, 291 energy states, 129 enthalpies of atomization of metallic elements, 133 equipoint (equivalent position), 318, 322 equivalent position, special, 319, 322 equivalent positions, assignment of atoms and groups to, 333, 336 equivalent positions, general, 318, 321 exchange integral, 52 excited-state chemistry, 113 exodentate multitopic ligand, 760 expectation value, 9

face-centered cubic (fcc), 364 Fermi energy, 129 ferric wheel, 753 f orbitals, cubic set, 296 f orbitals, general set, 295 f orbitals, nodal characteristics, 296 f orbitals, shapes, 295 ferrocene, 336, 337 first-order crystal field interactions, 270 fluorite, CaF2 , 370 form symbol, 301 fractional coordinates, 313, 317 free-electron model, 16 Friedel’s law, 321, 323 frontier orbital theory, 113 frozen core approximation, 148 fullerene adducts, 513 fullerene coordination compounds, 513

814

Index fullerene oligomers and polymers, 515 fullerene supramolecular adducts, 515 fullerene-C50 , 505 fullerene-C60 , 502 fullerene-C70 , 505 fullerene-C78 , geometric isomers, 505 fullerenes, 502 fullerenes, as π-ligands, 513 fullerenes, endohedral, 516 fullerenes, hetero, 516 fullerenic compounds, 511 fulleride salts, 514

Gaussian functions, 143 Gaussian-n (Gn) methods, 151 glide plane, axial, 309, 313 glide plane, diagonal, 309, 313 glide plane, diamond, 309, 313 glide plane, double, 310, 313 gold clusters, 721 gold(I)-thallium(I) interaction, 729 gold-xenon complexes, 678 graph-set descriptor, 743 graphical symbols for symmetry elements, 310, 313 graphite, hexagonal, 501 graphite, rhombohedral, 502 Grignard reagents, 454 ground-state chemistry, 113 guanidinium sulfonate, 744 guanidinium-carbonate, 749 guanidinium-trimesate, 749 guidance, N ,, -cyano-N , N -diisopropyl, 341, 344

Hückel molecular orbital theory, 110 Hückel theory for cyclic conjugated polyenes, 221, 228 halite, NaCl, 366 halogen anions, homopolyatomic, 654 halogen oxides, binary, 662 halogen oxides, ternary, 664 halogen oxoacids, 666 halogen, charge-transfer complex, 660 halogens, 654 Hamiltonian operator, 9 helicate, 754 hemicarcerand, 753, 804 hemoglobin, 618 Hermann-Mauguin notation, 301 heteronuclear diatomic molecules, 96 hexachlorocyclophosphazene, (PNCl3 )2 , 344, 346 hexaferrocenylbenzene, 510 hexagonal closest packing (hcp), 375

hexamethylbenzene, 340, 341 hexamethylenetetramine N -oxide, 359, 362 hexamethylenetetramine, (CH2 )6 N4 , 355, 358 hexamethylenetetramine, quaternized derivatives, 359, 363 hexanuclear clusters, 715 hexanuclear metal string cationic complexes, 727 hexatriene, cyclization, 114 high spin complexes, 264 high-nuclearity clusters, 717 homonuclear diatomic molecules, 92, 94 Hund’s rule, 60 hybrid orbitals, 100 hybrid orbitals, construction of, 232 hybridization schemes, 99, 232 hybridization schemes involving d orbitals, 234 hydrazine, 578 hydride complex, covalent metal, 417 hydride complex, high coordinate, 420 hydride complex, interstitial metal, 419 hydride complex, lanthanide, 421 hydride ion, 400 hydride ligand, five coordinate, 421 hydride ligand, four coordinate, 421 hydrido cluster complex, rhodium, 421 hydrogen bond, 401 hydrogen bond, geometry, 403 hydrogen bond, inverse, 415 hydrogen bond, non-conventional, 411 hydrogen bond, symmetrical, 406 hydrogen bond, X–H· · · H–M, 414 hydrogen bond, X–H· · · M, 412 hydrogen bond, X–H· · · π, 411 hydrogen bonding, generalized rules, 405 hydrogen bonding, universality and importance, 409 hydrogen bonds in organometallic compounds, 408 hydrogen bridged bond, 401 hydrogen carbonate dimer, 745 hydrogen molecular ion, 79, 82 hydrogen peroxide, 614 hydrogen, isotopes, 399 hydrogen, polymeric, 401 hydrogenic orbitals, 39 hydronium, 626 hydronium (or hydroxonium), 400 hydroxylamine, 578 hyperconjugation, 523

ices, high-pressure, 621 icosahedral groups, 177 identity element, 170 improper rotation axis, 169

Index induction interaction, 136 infinite square tube, 761 infrared (IR) activity, 237 inorganic supermolecule, 757 interfacial angles, 300 interhalogen compounds, 657 interhalogen ions, 659 intermetalloid cluster, 554 intermetalloid clusters of As and Bi, 606 intermolecular energy, 137 intermolecular interaction, 138, 733 interstitial heteroatoms, 718 intrinsic semiconductors, 130 inverse crown compounds, 457 inverse crown ether, 456 inversion axis, n-fold, 301 inversion center, 169 iodine compounds, polyvalent organic, 668 ionic bond, 121 ionic liquid, 126 ionic radii, 121 ionic size, 121 ionization energy, 64 iron(II) phthalocyanine, 341, 344 iron-sulfur cluster [Fe4 S4 (SC6 H5 )4 ]2− , 344, 345 irreducible representation, 180 iso-bond valence, 721 iso-structural clusters, 721 Kapustinskii equation, 125 Keesom energy, 135 kinetic energy operator, 12 Koch cluster, 368 krypton compounds, 679 lanthanide complexes, cyclopentadienyl, 694 lanthanide complexes, structures and properties, 694 lanthanide compounds, magnetic properties, 687 lanthanide contraction, 682 lanthanide(II) reduction chemistry, 699 lanthanides, 682 lanthanides, oxidation states, 684 lanthanides, term symbols, 685 lanthanum square antiprism, 763 Laplacian operator, 30 Laporte’s rule, 188 lattice (or space lattice), 305, 307 lattice energy, 124, 126 Laue groups (Laue classes), 325, 329 lead icosahedron, [Pt@Pb12 ]2− , 348, 350 Lennard-Jones 12-6 potential, 138 linear catenation, 494 linear combination of atomic orbitals, 77

815 linear combinations of ligand orbitals, AL4 molecule with Td symmetry, 228 linear homocatenated hexanuclear indium compound, 494 linear tape, 744 linear triatomic molecules, 99 lithium π complexes, 443 lithium alkoxides and aryloxides, 437 lithium amides, 438 lithium halide complexes, 439 lithium nitride, 435 lithium phosphide complexes, 441 lithium silicide complexes, 440 local spin density approximation (LSDA), 147 localized orbitals, 101 low spin complexes, 264 low-valent oxides and nitrides, 452

Madelung constant, 124 magnetic materials, 391 magnetic quantum number, 42 magnets, permanent, 393 many-electron atoms, 53 melamine, 744 melting points of chlorides salts, 127 melting points of metallic elements, 134 metaboric acid, 487 metal complex, X–H σ -bond coordination, 424 metal hydride, binary, 416 metal string molecules, 724 metal–metal bonds, 119 metal-based infinite chains and networks, 729 metal-metal bonds, 133 metal-organic framework (MOF), 799 metal-oxo complexes, 616 metallacarboranes with 14 and 15 vertices, 486 metallic bonds, 134 metallic radii, 132 metalloid cluster, 494 metalloid cluster, high-nuclearity, 553 methyllithium, (CH3 Li)4 , 357, 360 microstate, 58 Miller indices, 301 minimal basis set, 142 mixed gold-silver clusters, 724 mixed-valent silver(I,II) compound, 790 molecular Borromean link, 756 molecular capsule, 798 molecular container, 804 molecular hydrogen, coordinate bond, 402 molecular hydrogen, coordination compound, 422 molecular metal, 120 molecular necklace, 773 molecular orbital, 8 molecular orbital theory, 85

816

Index molecular orbital theory for octahedral complexes, 283 molecular orbital theory for square planar complexes, 289 molecular orbital theory, applications, 213 molecular orbital theory, essentials, 84 molecular panel, 765 molecular point group, 170 molecular polyhedra, 762 molecular recognition, 734 molecular skeleton, bond valence, 472 molecular term symbols, 189 molecular trefoil knot, 755 molecular vibrations, applications, 236 molecular wires, inorganic, 729 molten salt, 126 multi-configuration self-consistent field, 145 multiple bonding, between heavier Group 14 elements, 557 multiplicity, 318, 322 myoglobin, 618

nano-sized tubular section, 761 nanocapsule, 797, 798 nanocontainer, 804 nanoscale dodecahedron, 766 naphthacene radical cation, 520 naphthalene, 335, 337, 341, 343 nickel asenide, NiAs, 376 nickel wheel, 760 niobium monoxide, NbO, 368 nitric oxide, 573 nitride ion, N3− , 561 nitrogen, catenation of, 564 noble gas complexes, organometallic, 676 nitrogen oxides, 569 nitrosyl complexes, 574 nitrosyl halides, 573 nitrosyl salts, 573 noble gas atom, as donor ligand, 676 noble gas compounds, structural chemistry, 670 node, 758 non-benzenoid aromatic compound, 781 non-benzenoid aromatic compounds, 511 nonbonding molecular orbital, 84 normal modes, 236 normal vibration, 236 normalization constant, 8 normalization integral, 80

octahedral complexes, π bonding , 285 octahedral complexes,σ bonding, 283 octathio[8]circulene, C16 S8 , 511 oligo(α-pyridyl)amido ligand, 725

orbital energy level diagram, 97 order of the group, 184 organoaluminum compounds, 490 organoantimony compounds , 607 organobismuth compounds, 607 organolithium compounds, 443 organometallic compounds of Group 2 elements, 454 organometallic compounds, Group 13, 491 organometallic compounds, Group 13 containing M–M bonds, 492 organometallic compounds, of heavier Group 14 elements, 549 organouranium(IV) complex, dinuclear, 524 organoxenon compounds, 677 Orgel diagrams, 268 orthogonality, 8 orthonormality, 8 overlap integral, 80 oxide superconductors, 389 oxides of cyclic poly-sulfur, 637 oxides of sulfur, 634 oxides, of Ge, Sn and Pb, 546 oxo ligand, 616 oxo-acids of nitrogen, 575 oxo-centered Zn4 tetrahedron, 800 oxoacids of sulfur, 637 oxocarbon dianions, 781 oxoniobates, 369 oxonium, 626 oxygen, crystalline phases, 612 oxygen, singlet , 611 oxygenyl, 613 ozone, 614

Pn group, bond valence, 586 Pn groups, in metal complexes, 581 paramagnetic species, 95 particle in a one-dimensional box, 13 particle in a ring, 21 particle in a three-dimensional box, 17 particle in a triangle, 23 Pauli Exclusion Principle, 42 pentanitrogen cation, N+ 5 , 564 pentanuclear metal clusters, 715 perovskite, CaTiO3 , 385 peroxide, 610 perturbation methods, 146 phenylenediethynides, 794 phosphaalkenes, 596 phosphaalkynes, coordination modes, 597 phosphazanes, 591 phosphazenes, cyclic, 594 phosphazenes (phosphonitrilic compounds), 593 phosphazenes, generalizations, 596

Index phosphinidenes (phosphanylidenes), 596 phosphorus bonding types, 586 phosphorus, allotropic forms, 579 phosphorus, orthorhombic black, 344, 346 phosphorus, stereochemistry and bonding, 587 phosphorus–nitrogen compounds, 590 phosphorus-carbon compounds, 596 phosphorus-carbon compounds, π -coordination complexes , 600 physical properties of non-centrosymmetric materials, 304 Planck’s constant, 4 point group, 170 point group identification, flow chart, 178 point group identification, projection diagrams, 178 polarization functions, 143 polyatomic anions, of Ge, Sn and Pb, 547 polyiodides, 654 polyphosphide anions, 581 polypyridylamine, 725 polyrotaxane, 753, 773 polyselenides, 648 polysulfide, coordination compounds, 632 polysulfides, 631 polytellurides, 648 potassium octachlorodirhenate dihydrate, K2 [Re2 Cl8 ]·2H2 O, 341, 344 potential energy curves, 82 potential energy operator, 12 principal quantum number, 34 probability, 5, 39 probability density function, 6, 35 proper rotation, 167 pyrogallol[4]arene, 797

quadratic configuration interaction (QCI) method, 147 quadruple bond, 708 quantum mechanical operator, 15 quintuple bond, 712

racemic crystal, 338, 340 radial correlation, 47 radial equation, 42 radial function, 30, 33, 34 radial probability distribution function, 39 Raman (R) activity, 238 rare-earth cations, coordination geometries, 691 rare-earth metals, 682 rare-earth metals, crystalline forms, 683 rare-earth metals, halides, 689 rare-earth metals, organometallic compounds, 694

817 rare-earth metals, oxides, 688 rational indices, 301 reductive cyclotrimerization of CO, 524 relativistic effects, 64, 71, 72, 75, 133 resonance integral, 88 reticular design, 799 rhenium trioxide, ReO3 , 390 rhodizonate, 781 rhombic dodecahedron, 768 rhombohedral lattice, obverse setting, 306, 309 rhombohedral lattice, reverse setting, 306, 309 rings and clusters of Group 15 elements, 605 rock salt, NaCl, 366 rosette, 744 rosette ribbon, 745 rotation axis, 167 rotation-reflectionaxis, 169 rotaxane, 753 rule of mutual exclusion, 238 Russell-Saunders coupling, 56 Russell-Saunders terms, 56 rutile, TiO2 , 380

samarocene, decamethyl, 700 sandwich compound, metal monolayer, 520 Schönflies notaion, 301 Schrödinger equation, 18 Schrödinger equation for hydrogen atom, 29 screw axis, 309, 312 second-order crystal field interactions, 270 secondary building unit (SBU), 800 secular determinant, 90 secular equations, 90 selection rules in spectroscopy, 187 selenium allotropes, 644 selenium polyatomic cations, 644 selenium polymeric cations, 646 selenium stereochemistry, 649 self-consistent field (SCF) method, 54 semiconductors n-type, 130 semiconductors p-type, 130 semi-empirical methods, 142 separation constants, 30 sigma complexes, generalizations, 428 sigma-bond complexes, 428 silanes, 534 silatranes, 536 silicates, 540 silicates, general structural rules, 543 silicides, 534 silicon bridgehead, inverted tetrahedral bond configuration, 554 silicon dumbbell, unsubstituted, 554 silicon, octahedral hexa-coordinate, 536 silicon, stereochemistry, 535 silicon, structural chemistry, 533

818

Index silver acetylenediide, 531, 785 silver acetylide, 531, 785 silver carbide, 531 silver ethynide complexes, 792 silver iodide, AgI, 383 silver(I) arylethynide complexes, 796 silver(I) polyhedron, 785 silver-ethynide supramolecular synthons, 796 silyl anion radical, 539 silyl radical, 539 site of symmetry, 333 Slater-type orbital (STO), 143 sodium and potassium, π complexes, 445 sodium coordination complexes, 441 sodium thallide, 495 space group, polar, 376 space groups, 308, 312 space groups, commonly occurring, 319, 323 space groups, from systematic absences, 332 space groups, occurrence in crystals, 338, 340 space groups, symmetry diagrams, 317, 321 space-group diagrams, 316, 320 space-group symbol, Hermann-Mauguin nomenclature, 317, 321 space-group symbol, Schönflies notation, 317, 321 space-group symbols, 310, 316 space-group symmetry, application in crystal structure determination, 339, 341 spacer ligand, 758 spectrochemical series, 264 spectroscopic terms, 56, 60 spherical harmonics, 31 spin function, 48 spin multiplicity, 57 spin variable, 49 spin-orbit (L–S) coupling, 273 spin-orbit interaction, 62 spin-orbit interaction, first-order, 273 spin-orbit interaction, second-order, 273 spinel, inverse, 374 spinel, MgAl2 O4 , 359, 363, 373 split valence basis set, 143 splitting pattern of d orbitals in square planar complex, 266 splitting pattern of d orbitals in tetragonally distorted octahedral complex, 265 splitting pattern of f orbitals in tetrahedral crystal field, 298 splitting pattern of d orbitals in octahedral complex, 262 splitting pattern of d orbitals in tetrahedral complex, 262 splitting pattern of f orbitals in octahedral crystal field , 298 stacking, π –π , 796 standing wave, 10

stereochemistry of As, Sb and Bi, 602 stereographic projection, 303 steric strain, 522 strong crystal field, 279 strong field ligands, 266 structure-property correlation, 118 subnitrides, 453 subvalent halides, of heavier Group 14 elements, 544 sucrose, 340, 343 sulfide, coordination modes, 631 sulfur allotropes, 627 sulfur oxides, 635 sulfur, oxoacids, 637 sulfur, polyatomic cations, 630 sulfur-nitrogen compounds, 641 super inverse crown ether, 457 super-adamantoid cage, 765 supermolecule, 733 superoxide, 610 supramolecular capsule, 799 supramolecular chemistry, 733 supramolecular rosette, 745 supramolecular self-assembly, 735 supramolecular synthon, 737 symmetries and activities of the normal modes, 236 symmetry elements, 167 symmetry operations, 167 symmetry plane, 168 synthon X · · · X trimer, 738 systemic absences, 328, 329

Tanabe–Sugano diagrams, 274 tellurium polyatomic cations, 644 tellurium polymeric cations, 646 tellurium stereochemistry, 649 term symbols, 56 tetrahedral iron(II) host–guest complex, 762 tetranuclear clusters, 714 tetraphenylporphinato)iron(II),meso-, 347, 350 thallium naked anion clusters, 496 thermochemical radii, 126 thioallophanate, 3-, 781 tin metalloid cluster, high-nuclearity, 554 torsion angle, 315, 317 total wavefunctions of atomic orbitals with n = 1−4, 35 totally symmetric representation, 181 transition-metal clusters, 703 transitions d–d, 271 trefoil knot, 753 triazine, -s, 350, 349, 351 trimethylaluminum, Al2 Me6 , 343, 344

Index trinuclear clusters, 713 triple zeta basis set, 143 Uncertainty Principle, 16 unit cell, 306–308 unit cell transformation, 307, 310 unstable inorganic/organic anions, stabilization of, 780 unsupported In-In single bonds, 494 uranocene, 341, 343, 519 urea, 345, 347 urea, non-stoichiometric inclusion compounds, 350, 352 urea/thiourea complexes, 780 valence band, 129, 130 valence bond theory, 86, 100 valence tautomer, 782 van der Waals forces, 135 van der Waals interaction, 135 van der Waals interactions, 135 van der Waals radii, 139 variational method, 46, 86 vector sum, 57 vertical detachment energies (VDEs), 155 vibrational spectra of benzene, 254 vibrational spectra of five-atom molecules, 244

819 vibrational spectra of linear molecules, 252 vibronic interaction in transition metal complexes, 294 virial theorem, 13

Wade’s rules, 474 water, 620 water, liquid, 623 wave equation, 6 weak crystal field, 279 weak field ligands, 266 Weizmann-n (Wn) methods, 152 Woodward–Hoffmann rules, 113 Wyckoff notation, 318, 322

xenon difluoride, XeF2 , 346, 348 xenon fluorides, bonding description, 672 xenon fluorides, complexes of, 674 xenon, stereochemistry, 671

zeolites, 542 zinc sulfide, cubic form, zinc blende, sphalerite, 371 zinc sulfide, hexagonal form, wurtzite, 376 Zintl phases, 496 zircon, ZrO2 , 371